Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1112 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22574349 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22569556 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #22562232 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #22562229 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #22562226 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22561891 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C67×#2202 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16864233 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | #16864192 | — | 2 | 3 | no | — |
| 10 | #16864146 | C22 | 1 | 3 | yes | complemented |
| 11 | #16864140 | — | 2 | 3 | no | — |
| 12 | #16864135 | — | 2 | 3 | no | — |
| 13 | #16863945 | C22 | 1 | 3 | yes | — |
| 14 | #16863925 | — | 2 | 3 | no | — |
| 15 | #16863902 | — | 2 | 3 | no | — |
| 16 | #16863581 | C22 | 1 | 3 | yes | complemented |
| 17 | #16863579 | C22 | 1 | 3 | yes | complemented |
| 18 | #16863575 | — | 2 | 3 | no | — |
| 19 | #16863568 | C22 | 1 | 3 | yes | — |
| 20 | #16863562 | — | 2 | 3 | no | — |
| 21 | #104×D67 | — | 2 | 3 | no | — |
| 22 | #16863379 | C22 | 1 | 3 | yes | complemented |
| 23 | #16863194 | C22 | 1 | 6 | yes | complemented |
| 24 | #16863193 | C22 | 1 | 3 | yes | complemented |
| 25 | H(3,𝔽4)×C67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #454×C67 | C22 | 1 | 3 | yes | — |
| 27 | #355×C67 | C22 | 1 | 3 | yes | complemented |
| 28 | #14524091 | — | 4 | 1 | no | — |
| 29 | #14524091 | C23 | 1 | 1 | yes | characteristic |
| 30 | #14524089 | — | 2 | 3 | no | — |
| 31 | #14524089 | — | 4 | 1 | no | — |
| 32 | C2×#11761629 | — | 4 | 1 | no | — |
| 33 | C2×#11761629 | C23 | 1 | 1 | yes | characteristic |
| 34 | C2×#11761627 | D4 | 1 | 3 | yes | — |
| 35 | #41×D67 | — | 2 | 3 | no | — |
| 36 | #41×D67 | — | 4 | 1 | no | — |
| 37 | C23×Dic67 | — | 2 | 1 | no | — |
| 38 | #14524076 | — | 2 | 3 | no | — |
| 39 | #14524073 | — | 2 | 3 | no | — |
| 40 | #14524072 | — | 4 | 3 | no | — |
| 41 | #14524069 | — | 2 | 3 | no | — |
| 42 | #14524067 | — | 4 | 3 | no | — |
| 43 | #14524064 | — | 4 | 3 | no | — |
| 44 | #14524062 | — | 4 | 3 | no | — |
| 45 | M16×D67 | — | 2 | 3 | no | — |
| 46 | #14524041 | C23 | 1 | 3 | yes | — |
| 47 | #14524039 | D4 | 1 | 3 | yes | — |
| 48 | #14524036 | — | 2 | 6 | no | — |
| 49 | #14524035 | — | 2 | 3 | no | — |
| 50 | #14524031 | D4 | 1 | 3 | yes | — |
| 51 | #14524027 | — | 2 | 3 | no | — |
| 52 | #14524025 | — | 2 | 6 | no | — |
| 53 | #14524024 | — | 2 | 3 | no | — |
| 54 | #14524020 | — | 2 | 6 | no | — |
| 55 | #14524019 | — | 2 | 3 | no | — |
| 56 | #14524016 | — | 2 | 6 | no | — |
| 57 | #14524015 | — | 2 | 6 | no | — |
| 58 | #14524014 | — | 2 | 3 | no | — |
| 59 | #14524012 | — | 2 | 3 | no | — |
| 60 | Q8×Dic67 | — | 2 | 1 | no | — |
| 61 | D4×Dic67 | — | 2 | 3 | no | — |
| 62 | (C22⋊D67)⋊C4 | — | 2 | 6 | no | — |
| 63 | #14523999 | — | 2 | 3 | no | — |
| 64 | C42×D67 | D4 | 1 | 3 | yes | — |
| 65 | #14523971 | — | 2 | 3 | no | — |
| 66 | #14523970 | — | 2 | 3 | no | — |
| 67 | #14523969 | — | 2 | 3 | no | — |
| 68 | #14523962 | C23 | 1 | 3 | yes | — |
| 69 | #14523959 | — | 2 | 3 | no | — |
| 70 | 2−1+4×C67 | C23 | 1 | 1 | yes | characteristic |
| 71 | AGL(1,ℤ/8)×C67 | — | 2 | 3 | no | — |
| 72 | #124×C67 | — | 2 | 3 | no | — |
| 73 | #124×C67 | C23 | 1 | 3 | yes | — |
| 74 | #120×C67 | — | 2 | 3 | no | — |
| 75 | #104×C67 | — | 2 | 3 | no | — |
| 76 | #101×C67 | C23 | 1 | 3 | yes | — |
| 77 | #11761629 | — | 2 | 3 | no | — |
| 78 | #11761629 | — | 4 | 1 | no | — |
| 79 | #11761629 | — | 4 | 1 | no | — |
| 80 | #11761629 | — | 4 | 1 | no | — |
| 81 | #11761629 | — | 4 | 3 | no | — |
| 82 | #11761628 | — | 2 | 3 | no | — |
| 83 | #11761628 | — | 4 | 3 | no | — |
| 84 | #11761628 | — | 4 | 3 | no | — |
| 85 | #11761627 | — | 2 | 3 | no | — |
| 86 | #11761627 | — | 4 | 3 | no | — |
| 87 | #11761627 | — | 4 | 3 | no | — |
| 88 | #11761627 | — | 4 | 1 | no | — |
| 89 | C2×Dic134 | C2×D4 | 1 | 3 | yes | — |
| 90 | Q8×D67 | — | 2 | 3 | no | — |
| 91 | Q8×D67 | — | 4 | 1 | no | — |
| 92 | C2×D268 | — | 4 | 3 | no | — |
| 93 | C2×D268 | C2×D4 | 1 | 3 | yes | — |
| 94 | C2×C22⋊D67 | — | 2 | 6 | no | — |
| 95 | C2×C22⋊D67 | — | 2 | 3 | no | — |
| 96 | D4×D67 | — | 2 | 3 | no | — |
| 97 | D4×D67 | — | 4 | 3 | no | — |
| 98 | D4×D67 | — | 4 | 3 | no | — |
| 99 | C22×Dic67 | — | 2 | 3 | no | — |
| 100 | C22×Dic67 | — | 2 | 3 | no | — |
| 101 | C22×Dic67 | — | 8 | 1 | no | — |
| 102 | C22×Dic67 | — | 8 | 1 | no | — |
| 103 | C2×C4×D67 | — | 2 | 3 | no | — |
| 104 | C2×C4×D67 | — | 4 | 3 | no | — |
| 105 | C2×C4×D67 | C2×D4 | 1 | 3 | yes | — |
| 106 | Dic268 | — | 4 | 3 | no | — |
| 107 | #11761618 | — | 4 | 3 | no | — |
| 108 | #11761617 | — | 4 | 3 | no | — |
| 109 | #11761616 | — | 4 | 3 | no | — |
| 110 | #11761616 | — | 4 | 3 | no | — |
| 111 | #11761613 | — | 4 | 3 | no | — |
| 112 | #11761612 | — | 2 | 3 | no | — |
| 113 | #11761611 | — | 4 | 3 | no | — |
| 114 | C8×D67 | — | 4 | 3 | no | — |
| 115 | C4⋊Dic67 | — | 2 | 3 | no | — |
| 116 | C4⋊Dic67 | — | 2 | 3 | no | — |
| 117 | Dic67⋊C4 | — | 2 | 6 | no | — |
| 118 | Dic67⋊C4 | — | 2 | 6 | no | — |
| 119 | C22⋊Dic67 | — | 2 | 3 | no | — |
| 120 | C22⋊Dic67 | — | 2 | 6 | no | — |
| 121 | (C2×D67)⋊C4 | — | 2 | 6 | no | — |
| 122 | C4×Dic67 | — | 2 | 3 | no | — |
| 123 | C4×Dic67 | C2×D4 | 1 | 3 | yes | — |
| 124 | C24×C67 | — | 2 | 1 | no | — |
| 125 | #41×C67 | — | 2 | 3 | no | — |
| 126 | #41×C67 | — | 4 | 1 | no | — |
| 127 | C2×Q8×C67 | — | 2 | 1 | no | — |
| 128 | C2×Q8×C67 | — | 4 | 1 | no | — |
| 129 | C2×Q8×C67 | C24 | 1 | 1 | yes | characteristic |
| 130 | C2×D4×C67 | — | 2 | 3 | no | — |
| 131 | C2×D4×C67 | C2×D4 | 1 | 3 | yes | — |
| 132 | SD16×C67 | — | 4 | 3 | no | — |
| 133 | D8×C67 | — | 4 | 3 | no | — |
| 134 | M16×C67 | — | 2 | 3 | no | — |
| 135 | C22⋊C4×C67 | — | 2 | 3 | no | — |
| 136 | C22⋊C4×C67 | — | 2 | 6 | no | — |
| 137 | C42×C67 | C2×D4 | 1 | 3 | yes | — |
| 138 | C23×C67 | — | 2 | 3 | no | — |
| 139 | C23×C67 | — | 8 | 2 | no | — |
| 140 | C23×C67 | — | 8 | 1 | no | — |
| 141 | C22×D67 | — | 4 | 3 | no | — |
| 142 | C22×D67 | #120 | 1 | 3 | yes | — |
| 143 | Q8×C67 | — | 2 | 3 | no | — |
| 144 | Q8×C67 | — | 4 | 1 | no | — |
| 145 | Q8×C67 | — | 8 | 1 | no | — |
| 146 | D4×C67 | — | 2 | 3 | no | — |
| 147 | D4×C67 | — | 4 | 3 | no | — |
| 148 | D4×C67 | — | 4 | 1 | no | — |
| 149 | D4×C67 | — | 8 | 3 | no | — |
| 150 | C2×C4×C67 | — | 2 | 3 | no | — |
| 151 | C2×C4×C67 | — | 4 | 3 | no | — |
| 152 | C2×C4×C67 | C22×D4 | 1 | 3 | yes | — |
| 153 | C22⋊D67 | — | 4 | 3 | no | — |
| 154 | C22⋊D67 | — | 4 | 1 | no | — |
| 155 | C22⋊D67 | — | 4 | 1 | no | — |
| 156 | C22⋊D67 | — | 8 | 3 | no | — |
| 157 | C22⋊D67 | — | 8 | 6 | no | — |
| 158 | C2×Dic67 | — | 2 | 3 | no | — |
| 159 | C2×Dic67 | — | 2 | 3 | no | — |
| 160 | C2×Dic67 | — | 4 | 1 | no | — |
| 161 | C2×Dic67 | — | 4 | 3 | no | — |
| 162 | C2×Dic67 | — | 4 | 3 | no | — |
| 163 | C2×Dic67 | — | 8 | 3 | no | — |
| 164 | C2×Dic67 | #120 | 1 | 1 | yes | characteristic |
| 165 | D268 | — | 2 | 3 | no | — |
| 166 | D268 | — | 4 | 3 | no | — |
| 167 | D268 | — | 4 | 3 | no | — |
| 168 | C4×D67 | — | 2 | 3 | no | — |
| 169 | C4×D67 | — | 2 | 3 | no | — |
| 170 | C4×D67 | — | 4 | 3 | no | — |
| 171 | C4×D67 | — | 4 | 3 | no | — |
| 172 | C4×D67 | — | 4 | 1 | no | — |
| 173 | C4×D67 | — | 8 | 3 | no | — |
| 174 | Dic134 | — | 2 | 3 | no | — |
| 175 | Dic134 | — | 4 | 1 | no | — |
| 176 | Dic134 | — | 4 | 3 | no | — |
| 177 | C8×C67 | — | 4 | 3 | no | — |
| 178 | C67⋊C8 | — | 4 | 3 | no | — |
| 179 | C22×C67 | — | 4 | 6 | no | — |
| 180 | C22×C67 | — | 4 | 3 | no | — |
| 181 | C22×C67 | — | 4 | 1 | no | — |
| 182 | C22×C67 | — | 8 | 4 | no | — |
| 183 | C22×C67 | C2×#120 | 1 | 1 | yes | characteristic |
| 184 | C2×D67 | — | 2 | 3 | no | — |
| 185 | C2×D67 | — | 4 | 3 | no | — |
| 186 | C2×D67 | — | 4 | 1 | no | — |
| 187 | C2×D67 | — | 16 | 3 | no | — |
| 188 | C4×C67 | — | 2 | 3 | no | — |
| 189 | C4×C67 | — | 4 | 3 | no | — |
| 190 | C4×C67 | — | 4 | 1 | no | — |
| 191 | Dic67 | — | 4 | 3 | no | — |
| 192 | Dic67 | — | 4 | 1 | no | — |
| 193 | Dic67 | — | 4 | 3 | no | — |
| 194 | Dic67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 195 | Dic67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 196 | #33564 | — | 67 | 1 | no | maximal, Sylow |
| 197 | C2×C67 | — | 2 | 1 | no | — |
| 198 | C2×C67 | — | 8 | 1 | no | — |
| 199 | C2×C67 | — | 8 | 3 | no | — |
| 200 | C2×C67 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 201 | D67 | — | 4 | 3 | no | — |
| 202 | D67 | — | 8 | 1 | no | — |
| 203 | #3529 | — | 67 | 1 | no | — |
| 204 | #3018 | — | 67 | 3 | no | — |
| 205 | #2203 | — | 67 | 3 | no | — |
| 206 | #2203 | — | 67 | 3 | no | — |
| 207 | #2202 | — | 67 | 1 | no | — |
| 208 | #2202 | D67 | 1 | 1 | yes | characteristic, complemented |
| 209 | #2132 | — | 67 | 3 | no | — |
| 210 | C67 | #33564 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 211 | #585 | — | 67 | 1 | no | — |
| 212 | #575 | — | 134 | 3 | no | — |
| 213 | #563 | — | 67 | 3 | no | — |
| 214 | #562 | — | 134 | 3 | no | — |
| 215 | H(3,𝔽4) | C2×D67 | 1 | 1 | yes | characteristic, complemented |
| 216 | #560 | — | 134 | 3 | no | — |
| 217 | #532 | — | 67 | 3 | no | — |
| 218 | #529 | — | 134 | 3 | no | — |
| 219 | #525 | — | 134 | 3 | no | — |
| 220 | #456 | — | 67 | 3 | no | — |
| 221 | #456 | — | 67 | 3 | no | — |
| 222 | #455 | — | 134 | 3 | no | — |
| 223 | #454 | — | 67 | 3 | no | — |
| 224 | #454 | C2×D67 | 1 | 3 | yes | — |
| 225 | #453 | — | 134 | 3 | no | — |
| 226 | C2×#104 | — | 134 | 3 | no | — |
| 227 | #413 | — | 67 | 3 | no | — |
| 228 | #356 | — | 67 | 6 | no | — |
| 229 | #355 | — | 67 | 3 | no | — |
| 230 | #355 | C2×D67 | 1 | 3 | yes | complemented |
| 231 | 2−1+4 | — | 268 | 1 | no | — |
| 232 | 2−1+4 | — | 67 | 1 | no | — |
| 233 | 2−1+4 | C22×D67 | 1 | 1 | yes | characteristic |
| 234 | H(5,𝔽2) | — | 268 | 1 | no | — |
| 235 | H(5,𝔽2) | — | 134 | 3 | no | — |
| 236 | C2×#41 | — | 268 | 1 | no | — |
| 237 | C2×#41 | — | 268 | 1 | no | — |
| 238 | C2×#41 | — | 67 | 1 | no | — |
| 239 | C2×#41 | — | 67 | 3 | no | — |
| 240 | C2×#41 | — | 134 | 3 | no | — |
| 241 | C23×C4 | — | 134 | 1 | no | — |
| 242 | #137 | — | 268 | 3 | no | — |
| 243 | #137 | — | 134 | 3 | no | — |
| 244 | #137 | — | 134 | 3 | no | — |
| 245 | AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 246 | AGL(1,ℤ/8) | — | 268 | 3 | no | — |
| 247 | AGL(1,ℤ/8) | — | 134 | 3 | no | — |
| 248 | #135 | — | 268 | 3 | no | — |
| 249 | #135 | — | 268 | 3 | no | — |
| 250 | C2×M16 | — | 134 | 3 | no | — |
| 251 | C4⋊Q8 | — | 67 | 3 | no | — |
| 252 | #127 | — | 67 | 3 | no | — |
| 253 | #126 | — | 134 | 6 | no | — |
| 254 | #125 | — | 134 | 3 | no | — |
| 255 | #124 | — | 2 | 3 | no | — |
| 256 | #124 | — | 67 | 3 | no | — |
| 257 | #124 | C22×D67 | 1 | 3 | yes | — |
| 258 | #123 | — | 134 | 3 | no | — |
| 259 | #123 | — | 134 | 6 | no | — |
| 260 | #123 | — | 134 | 3 | no | — |
| 261 | C22⋊Q8 | — | 134 | 6 | no | — |
| 262 | C22⋊Q8 | — | 134 | 3 | no | — |
| 263 | #121 | — | 134 | 6 | no | — |
| 264 | #121 | — | 134 | 6 | no | — |
| 265 | #121 | — | 134 | 3 | no | — |
| 266 | #120 | — | 2 | 3 | no | — |
| 267 | #120 | — | 134 | 3 | no | — |
| 268 | C4×Q8 | — | 134 | 1 | no | — |
| 269 | C4×D4 | — | 134 | 6 | no | — |
| 270 | C4×D4 | — | 134 | 3 | no | — |
| 271 | #117 | — | 134 | 3 | no | — |
| 272 | C2×C42 | — | 67 | 3 | no | — |
| 273 | #104 | — | 2 | 3 | no | — |
| 274 | #104 | — | 134 | 3 | no | — |
| 275 | #104 | — | 134 | 3 | no | — |
| 276 | #104 | — | 134 | 3 | no | — |
| 277 | #101 | — | 67 | 3 | no | — |
| 278 | #101 | C22×D67 | 1 | 3 | yes | — |
| 279 | #100 | — | 134 | 3 | no | — |
| 280 | C24 | — | 2 | 1 | no | — |
| 281 | #41 | — | 2 | 3 | no | — |
| 282 | #41 | — | 4 | 1 | no | — |
| 283 | #41 | — | 268 | 3 | no | — |
| 284 | #41 | — | 268 | 3 | no | — |
| 285 | #41 | — | 268 | 3 | no | — |
| 286 | #41 | — | 268 | 1 | no | — |
| 287 | #41 | — | 268 | 1 | no | — |
| 288 | #41 | — | 268 | 3 | no | — |
| 289 | #41 | — | 268 | 3 | no | — |
| 290 | #41 | — | 268 | 1 | no | — |
| 291 | #41 | — | 268 | 1 | no | — |
| 292 | #41 | — | 134 | 3 | no | — |
| 293 | #41 | — | 134 | 3 | no | — |
| 294 | #41 | — | 134 | 3 | no | — |
| 295 | C2×Q8 | — | 2 | 1 | no | — |
| 296 | C2×Q8 | — | 4 | 1 | no | — |
| 297 | C2×Q8 | — | 268 | 1 | no | — |
| 298 | C2×Q8 | — | 67 | 3 | no | — |
| 299 | C2×Q8 | — | 134 | 3 | no | — |
| 300 | C2×Q8 | C23×D67 | 1 | 1 | yes | characteristic |
| 301 | C2×D4 | — | 2 | 3 | no | — |
| 302 | C2×D4 | — | 268 | 3 | no | — |
| 303 | C2×D4 | — | 268 | 3 | no | — |
| 304 | C2×D4 | — | 268 | 3 | no | — |
| 305 | C2×D4 | — | 67 | 3 | no | — |
| 306 | C2×D4 | — | 134 | 3 | no | — |
| 307 | C2×D4 | — | 134 | 6 | no | — |
| 308 | C2×D4 | — | 134 | 3 | no | — |
| 309 | C2×D4 | D4×D67 | 1 | 3 | yes | — |
| 310 | C22×C4 | — | 268 | 3 | no | — |
| 311 | C22×C4 | — | 536 | 1 | no | — |
| 312 | C22×C4 | — | 536 | 1 | no | — |
| 313 | C22×C4 | — | 67 | 3 | no | — |
| 314 | C22×C4 | — | 134 | 3 | no | — |
| 315 | C22×C4 | — | 134 | 3 | no | — |
| 316 | C22×C4 | — | 134 | 3 | no | — |
| 317 | Q16 | — | 268 | 3 | no | — |
| 318 | Q16 | — | 268 | 3 | no | — |
| 319 | SD16 | — | 4 | 3 | no | — |
| 320 | SD16 | — | 268 | 3 | no | — |
| 321 | SD16 | — | 268 | 3 | no | — |
| 322 | SD16 | — | 268 | 3 | no | — |
| 323 | D8 | — | 4 | 3 | no | — |
| 324 | D8 | — | 268 | 3 | no | — |
| 325 | M16 | — | 2 | 3 | no | — |
| 326 | M16 | — | 268 | 3 | no | — |
| 327 | M16 | — | 134 | 3 | no | — |
| 328 | C2×C8 | — | 268 | 3 | no | — |
| 329 | C4⋊C4 | — | 134 | 6 | no | — |
| 330 | C4⋊C4 | — | 134 | 3 | no | — |
| 331 | C4⋊C4 | — | 134 | 3 | no | — |
| 332 | C4⋊C4 | — | 134 | 6 | no | — |
| 333 | C22⋊C4 | — | 2 | 3 | no | — |
| 334 | C22⋊C4 | — | 2 | 6 | no | — |
| 335 | C22⋊C4 | — | 134 | 6 | no | — |
| 336 | C22⋊C4 | — | 134 | 3 | no | — |
| 337 | C22⋊C4 | — | 134 | 6 | no | — |
| 338 | C42 | — | 67 | 3 | no | — |
| 339 | C42 | — | 134 | 3 | no | — |
| 340 | C42 | D4×D67 | 1 | 3 | yes | — |
| 341 | C23 | — | 2 | 3 | no | — |
| 342 | C23 | — | 8 | 1 | no | — |
| 343 | C23 | — | 8 | 2 | no | — |
| 344 | C23 | — | 268 | 3 | no | — |
| 345 | C23 | — | 67 | 3 | no | — |
| 346 | Q8 | — | 2 | 3 | no | — |
| 347 | Q8 | — | 4 | 1 | no | — |
| 348 | Q8 | — | 8 | 1 | no | — |
| 349 | Q8 | — | 268 | 3 | no | — |
| 350 | Q8 | — | 268 | 1 | no | — |
| 351 | Q8 | — | 134 | 3 | no | — |
| 352 | D4 | — | 2 | 3 | no | — |
| 353 | D4 | — | 4 | 3 | no | — |
| 354 | D4 | — | 4 | 1 | no | — |
| 355 | D4 | — | 8 | 3 | no | — |
| 356 | D4 | — | 268 | 3 | no | — |
| 357 | D4 | — | 268 | 3 | no | — |
| 358 | D4 | — | 268 | 3 | no | — |
| 359 | D4 | — | 268 | 1 | no | — |
| 360 | D4 | — | 268 | 1 | no | — |
| 361 | D4 | — | 536 | 6 | no | — |
| 362 | D4 | — | 536 | 3 | no | — |
| 363 | D4 | — | 134 | 3 | no | — |
| 364 | C2×C4 | — | 2 | 3 | no | — |
| 365 | C2×C4 | — | 4 | 3 | no | — |
| 366 | C2×C4 | — | 268 | 3 | no | — |
| 367 | C2×C4 | — | 268 | 3 | no | — |
| 368 | C2×C4 | — | 268 | 1 | no | — |
| 369 | C2×C4 | — | 268 | 1 | no | — |
| 370 | C2×C4 | — | 268 | 3 | no | — |
| 371 | C2×C4 | — | 268 | 3 | no | — |
| 372 | C2×C4 | — | 536 | 3 | no | — |
| 373 | C2×C4 | — | 536 | 3 | no | — |
| 374 | C2×C4 | — | 67 | 1 | no | — |
| 375 | C2×C4 | — | 134 | 3 | no | — |
| 376 | C2×C4 | — | 134 | 3 | no | — |
| 377 | C2×C4 | — | 134 | 3 | no | — |
| 378 | C2×C4 | — | 134 | 3 | no | — |
| 379 | C2×C4 | C2×D4×D67 | 1 | 3 | yes | — |
| 380 | C8 | — | 4 | 3 | no | — |
| 381 | C8 | — | 268 | 3 | no | — |
| 382 | C22 | — | 4 | 6 | no | — |
| 383 | C22 | — | 4 | 1 | no | — |
| 384 | C22 | — | 4 | 3 | no | — |
| 385 | C22 | — | 8 | 4 | no | — |
| 386 | C22 | — | 268 | 3 | no | — |
| 387 | C22 | — | 268 | 1 | no | — |
| 388 | C22 | — | 1072 | 3 | no | — |
| 389 | C22 | — | 134 | 3 | no | — |
| 390 | C22 | #120×D67 | 1 | 1 | yes | characteristic |
| 391 | C4 | — | 2 | 3 | no | — |
| 392 | C4 | — | 4 | 3 | no | — |
| 393 | C4 | — | 4 | 1 | no | — |
| 394 | C4 | — | 268 | 3 | no | — |
| 395 | C4 | — | 268 | 1 | no | — |
| 396 | C4 | — | 268 | 3 | no | — |
| 397 | C4 | — | 67 | 1 | no | — |
| 398 | C4 | — | 67 | 1 | no | — |
| 399 | C2 | — | 2 | 1 | no | — |
| 400 | C2 | — | 8 | 3 | no | — |
| 401 | C2 | — | 8 | 1 | no | — |
| 402 | C2 | — | 268 | 3 | no | — |
| 403 | C2 | — | 536 | 1 | no | — |
| 404 | C2 | B(4,𝔽2)×D67 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22574349 | C2 | semidirect |
| 2. #22569556 | C2 | semidirect |
| 3. #22562232 | C2 | semidirect |
| 4. #22562229 | C2 | semidirect |
| 5. #22562226 | C2 | semidirect |
| 6. #22561891 | C2 | semidirect |
| 7. C67×#2202 | C2 | semidirect |
| 8. #16864233 | C22 | semidirect |
| 10. #16864146 | C22 | semidirect |
| 16. #16863581 | C22 | semidirect |
| 17. #16863579 | C22 | semidirect |
| 22. #16863379 | C22 | semidirect |
| 23. #16863194 | C22 | semidirect |
| 24. #16863193 | C22 | semidirect |
| 25. H(3,𝔽4)×C67 | C22 | semidirect |
| 27. #355×C67 | C22 | semidirect |
| 208. #2202 | D67 | semidirect |
| 210. C67 | #33564 | semidirect |
| 215. H(3,𝔽4) | C2×D67 | semidirect |
| 230. #355 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574349 | 2 |
| #22569556 | 2 |
| #22562232 | 2 |
| #22562229 | 2 |
| #22562226 | 2 |
| #22561891 | 2 |
| C67×#2202 | 2 |
| #33564 | 67 |