Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
828 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 133 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 | C2×#16863592 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22565125 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22561014 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#16863123 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C67×#1296 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C22×D536 | — | 2 | 2 | no | — |
| 7 | C2×#14524040 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×#14524018 | — | 2 | 2 | no | — |
| 9 | C2×C4×D268 | C22 | 1 | 2 | yes | — |
| 10 | #16863592 | — | 2 | 4 | no | — |
| 11 | #16863592 | — | 2 | 4 | no | — |
| 12 | C2×#14523965 | — | 2 | 2 | no | — |
| 13 | C2×#14523963 | — | 2 | 2 | no | — |
| 14 | C2×C4×C67⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16863313 | — | 2 | 2 | no | — |
| 16 | #16863253 | — | 2 | 2 | no | — |
| 17 | #16863123 | — | 2 | 4 | no | — |
| 18 | C2×C4⋊C8×C67 | C22 | 1 | 2 | yes | — |
| 19 | #384×C67 | C22 | 1 | 1 | yes | characteristic |
| 20 | C22×D268 | — | 2 | 2 | no | — |
| 21 | C22×D268 | — | 2 | 1 | no | — |
| 22 | C22×D268 | — | 2 | 2 | no | — |
| 23 | C22×D268 | D4 | 1 | 2 | yes | — |
| 24 | C22×C4×D67 | — | 2 | 2 | no | — |
| 25 | C2×D536 | — | 2 | 8 | no | — |
| 26 | C2×D536 | — | 4 | 4 | no | — |
| 27 | C2×D536 | — | 4 | 4 | no | — |
| 28 | C22×C67⋊C8 | — | 2 | 1 | no | — |
| 29 | #14524040 | — | 2 | 2 | no | — |
| 30 | #14524040 | — | 2 | 1 | no | — |
| 31 | #14524040 | D4 | 1 | 2 | yes | complemented |
| 32 | #14524018 | — | 4 | 4 | no | — |
| 33 | #14524018 | — | 4 | 4 | no | — |
| 34 | C4×D268 | — | 2 | 2 | no | — |
| 35 | C4×D268 | — | 2 | 2 | no | — |
| 36 | C4×D268 | — | 2 | 2 | no | — |
| 37 | C4×D268 | — | 2 | 2 | no | — |
| 38 | C2×C4⋊Dic67 | D4 | 1 | 2 | yes | — |
| 39 | C2×(C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 40 | C2×(C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 41 | #14523965 | — | 2 | 8 | no | — |
| 42 | #14523963 | — | 4 | 4 | no | — |
| 43 | C4×C67⋊C8 | — | 2 | 2 | no | — |
| 44 | C67⋊#95 | — | 2 | 2 | no | — |
| 45 | C22×C8×C67 | — | 2 | 2 | no | — |
| 46 | C2×C4⋊C4×C67 | — | 2 | 2 | no | — |
| 47 | C2×C4⋊C4×C67 | D4 | 1 | 2 | yes | — |
| 48 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 49 | C4⋊C8×C67 | — | 2 | 2 | no | — |
| 50 | C4⋊C8×C67 | D4 | 1 | 4 | yes | complemented |
| 51 | C23×D67 | — | 2 | 2 | no | — |
| 52 | C23×D67 | — | 4 | 1 | no | — |
| 53 | C2×D268 | — | 2 | 2 | no | — |
| 54 | C2×D268 | — | 2 | 2 | no | — |
| 55 | C2×D268 | — | 2 | 2 | no | — |
| 56 | C2×D268 | — | 2 | 2 | no | — |
| 57 | C2×D268 | — | 2 | 4 | no | — |
| 58 | C2×D268 | — | 2 | 2 | no | — |
| 59 | C2×D268 | — | 2 | 2 | no | — |
| 60 | C2×D268 | — | 4 | 2 | no | — |
| 61 | C2×D268 | — | 4 | 2 | no | — |
| 62 | C2×D268 | — | 4 | 2 | no | — |
| 63 | C2×D268 | — | 4 | 2 | no | — |
| 64 | C2×D268 | — | 4 | 2 | no | — |
| 65 | C2×D268 | — | 4 | 2 | no | — |
| 66 | C2×D268 | — | 4 | 8 | no | — |
| 67 | C2×D268 | — | 4 | 2 | no | — |
| 68 | C2×D268 | — | 4 | 1 | no | — |
| 69 | C2×D268 | — | 8 | 2 | no | — |
| 70 | C2×D268 | D8 | 1 | 4 | yes | complemented |
| 71 | C22×Dic67 | — | 2 | 2 | no | — |
| 72 | C2×C4×D67 | — | 4 | 2 | no | — |
| 73 | C2×C4×D67 | — | 4 | 2 | no | — |
| 74 | C2×C4×D67 | — | 4 | 2 | no | — |
| 75 | C2×C4×D67 | — | 4 | 2 | no | — |
| 76 | C2×C4×D67 | — | 4 | 2 | no | — |
| 77 | C2×C4×D67 | — | 4 | 2 | no | — |
| 78 | D536 | — | 4 | 16 | no | — |
| 79 | C2×C67⋊C8 | — | 2 | 2 | no | — |
| 80 | C2×C67⋊C8 | — | 4 | 1 | no | — |
| 81 | C2×C67⋊C8 | — | 4 | 1 | no | — |
| 82 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 83 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 84 | (C2×D67)⋊C4 | — | 4 | 8 | no | — |
| 85 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 86 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 87 | C22×C4×C67 | — | 2 | 2 | no | — |
| 88 | C22×C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 89 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C2×C8×C67 | — | 2 | 4 | no | — |
| 91 | C2×C8×C67 | — | 4 | 2 | no | — |
| 92 | C2×C8×C67 | — | 4 | 2 | no | — |
| 93 | C4⋊C4×C67 | — | 4 | 2 | no | — |
| 94 | C4⋊C4×C67 | — | 4 | 2 | no | — |
| 95 | C4⋊C4×C67 | — | 4 | 2 | no | — |
| 96 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C42×C67 | C2×D4 | 1 | 2 | yes | — |
| 98 | C42×C67 | #41 | 1 | 1 | yes | characteristic |
| 99 | C23×C67 | #120 | 1 | 1 | yes | characteristic |
| 100 | C22×D67 | — | 2 | 4 | no | — |
| 101 | C22×D67 | — | 4 | 2 | no | — |
| 102 | C22×D67 | — | 4 | 2 | no | — |
| 103 | C22×D67 | — | 4 | 2 | no | — |
| 104 | C22×D67 | — | 4 | 2 | no | — |
| 105 | C22×D67 | — | 4 | 2 | no | — |
| 106 | C22×D67 | — | 4 | 2 | no | — |
| 107 | C22×D67 | — | 4 | 2 | no | — |
| 108 | C22×D67 | — | 8 | 2 | no | — |
| 109 | C22×D67 | — | 8 | 2 | no | — |
| 110 | C22×D67 | — | 8 | 1 | no | — |
| 111 | C22×D67 | — | 8 | 1 | no | — |
| 112 | C2×C4×C67 | — | 2 | 1 | no | — |
| 113 | C2×C4×C67 | — | 2 | 1 | no | — |
| 114 | C2×C4×C67 | — | 4 | 4 | no | — |
| 115 | C2×C4×C67 | — | 4 | 2 | no | — |
| 116 | C2×C4×C67 | #120 | 1 | 2 | yes | — |
| 117 | C2×C4×C67 | #121 | 1 | 1 | yes | characteristic |
| 118 | C2×C4×C67 | #121 | 1 | 2 | yes | — |
| 119 | C2×C4×C67 | #127 | 1 | 1 | yes | characteristic |
| 120 | C2×C4×C67 | C2×D8 | 1 | 2 | yes | — |
| 121 | C2×C4×C67 | #135 | 1 | 2 | yes | — |
| 122 | C2×C4×C67 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 123 | C2×C4×C67 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 124 | C2×Dic67 | — | 4 | 2 | no | — |
| 125 | C2×Dic67 | — | 4 | 2 | no | — |
| 126 | C2×Dic67 | — | 4 | 2 | no | — |
| 127 | D268 | — | 2 | 4 | no | — |
| 128 | D268 | — | 2 | 4 | no | — |
| 129 | D268 | — | 4 | 4 | no | — |
| 130 | D268 | — | 4 | 4 | no | — |
| 131 | D268 | — | 4 | 2 | no | — |
| 132 | D268 | — | 4 | 4 | no | — |
| 133 | D268 | — | 4 | 2 | no | — |
| 134 | D268 | — | 8 | 2 | no | — |
| 135 | D268 | — | 8 | 8 | no | — |
| 136 | D268 | — | 8 | 2 | no | — |
| 137 | D268 | — | 8 | 2 | no | — |
| 138 | C4×D67 | — | 8 | 2 | no | — |
| 139 | C4×D67 | — | 8 | 2 | no | — |
| 140 | C4×D67 | — | 8 | 2 | no | — |
| 141 | C4×D67 | — | 8 | 2 | no | — |
| 142 | C8×C67 | — | 4 | 4 | no | — |
| 143 | C67⋊C8 | — | 4 | 2 | no | — |
| 144 | C22×C67 | #392 | 1 | 1 | yes | characteristic |
| 145 | C22×C67 | #447 | 1 | 2 | yes | — |
| 146 | C22×C67 | #449 | 1 | 2 | yes | — |
| 147 | C22×C67 | #453 | 1 | 1 | yes | characteristic |
| 148 | C22×C67 | #454 | 1 | 1 | yes | characteristic |
| 149 | C2×D67 | — | 4 | 4 | no | — |
| 150 | C2×D67 | — | 4 | 4 | no | — |
| 151 | C2×D67 | — | 4 | 4 | no | — |
| 152 | C2×D67 | — | 8 | 2 | no | — |
| 153 | C2×D67 | — | 8 | 2 | no | — |
| 154 | C2×D67 | — | 8 | 2 | no | — |
| 155 | C2×D67 | — | 8 | 2 | no | — |
| 156 | C2×D67 | — | 8 | 4 | no | — |
| 157 | C2×D67 | — | 8 | 2 | no | — |
| 158 | C2×D67 | — | 16 | 1 | no | — |
| 159 | C2×D67 | — | 16 | 1 | no | — |
| 160 | C2×D67 | — | 16 | 2 | no | — |
| 161 | C4×C67 | — | 2 | 1 | no | — |
| 162 | C4×C67 | — | 2 | 1 | no | — |
| 163 | C4×C67 | — | 8 | 2 | no | — |
| 164 | C4×C67 | #447 | 1 | 2 | yes | — |
| 165 | C4×C67 | #449 | 1 | 2 | yes | — |
| 166 | C4×C67 | #466 | 1 | 2 | yes | — |
| 167 | C4×C67 | #469 | 1 | 2 | yes | — |
| 168 | Dic67 | — | 8 | 2 | no | — |
| 169 | #10228 | — | 67 | 1 | no | maximal, Sylow |
| 170 | C2×C67 | #1619 | 1 | 1 | yes | characteristic |
| 171 | C2×C67 | #1624 | 1 | 1 | yes | characteristic |
| 172 | C2×C67 | #1625 | 1 | 2 | yes | — |
| 173 | C2×C67 | #1999 | 1 | 2 | yes | — |
| 174 | C2×C67 | #2006 | 1 | 1 | yes | characteristic |
| 175 | D67 | — | 8 | 4 | no | — |
| 176 | D67 | — | 16 | 2 | no | — |
| 177 | C2×#459 | — | 67 | 2 | no | — |
| 178 | #2537 | — | 67 | 1 | no | — |
| 179 | #1957 | — | 67 | 1 | no | — |
| 180 | C2×D4⋊C8 | — | 67 | 2 | no | — |
| 181 | #1296 | D67 | 1 | 1 | yes | characteristic, complemented |
| 182 | C67 | #10228 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 183 | C22×D8 | — | 134 | 2 | no | — |
| 184 | C2×#127 | — | 67 | 1 | no | — |
| 185 | C2×#121 | — | 134 | 2 | no | — |
| 186 | C2×C4×D4 | — | 67 | 2 | no | — |
| 187 | #459 | — | 134 | 4 | no | — |
| 188 | #459 | — | 134 | 4 | no | — |
| 189 | C2×C4⋊C8 | C2×D67 | 1 | 2 | yes | — |
| 190 | C2×#102 | — | 134 | 2 | no | — |
| 191 | C2×#102 | — | 134 | 2 | no | — |
| 192 | C2×C4×C8 | — | 67 | 1 | no | — |
| 193 | #394 | — | 134 | 2 | no | — |
| 194 | #384 | C2×D67 | 1 | 1 | yes | characteristic |
| 195 | #380 | — | 134 | 2 | no | — |
| 196 | D4⋊C8 | — | 134 | 4 | no | — |
| 197 | C22×D4 | — | 67 | 2 | no | — |
| 198 | C22×D4 | — | 134 | 2 | no | — |
| 199 | C22×D4 | — | 134 | 2 | no | — |
| 200 | C22×D4 | — | 134 | 1 | no | — |
| 201 | C23×C4 | — | 134 | 2 | no | — |
| 202 | C2×D8 | — | 268 | 4 | no | — |
| 203 | C2×D8 | — | 268 | 4 | no | — |
| 204 | C2×D8 | — | 134 | 8 | no | — |
| 205 | C22×C8 | — | 2 | 2 | no | — |
| 206 | C22×C8 | — | 134 | 1 | no | — |
| 207 | #127 | — | 67 | 2 | no | — |
| 208 | #127 | — | 134 | 2 | no | — |
| 209 | #127 | — | 134 | 1 | no | — |
| 210 | #121 | — | 268 | 4 | no | — |
| 211 | #121 | — | 268 | 4 | no | — |
| 212 | C4×D4 | — | 134 | 2 | no | — |
| 213 | C4×D4 | — | 134 | 2 | no | — |
| 214 | C4×D4 | — | 134 | 2 | no | — |
| 215 | C4×D4 | — | 134 | 2 | no | — |
| 216 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 217 | C2×C4⋊C4 | — | 67 | 2 | no | — |
| 218 | C2×C4⋊C4 | D268 | 1 | 2 | yes | — |
| 219 | C2×C22⋊C4 | — | 134 | 4 | no | — |
| 220 | C2×C22⋊C4 | — | 134 | 2 | no | — |
| 221 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 222 | C4⋊C8 | — | 2 | 2 | no | — |
| 223 | C4⋊C8 | D268 | 1 | 4 | yes | complemented |
| 224 | #102 | — | 268 | 4 | no | — |
| 225 | #102 | — | 134 | 8 | no | — |
| 226 | C4×C8 | — | 134 | 2 | no | — |
| 227 | #95 | — | 134 | 2 | no | — |
| 228 | C24 | — | 268 | 1 | no | — |
| 229 | C24 | — | 134 | 2 | no | — |
| 230 | C2×D4 | — | 268 | 2 | no | — |
| 231 | C2×D4 | — | 268 | 2 | no | — |
| 232 | C2×D4 | — | 268 | 8 | no | — |
| 233 | C2×D4 | — | 268 | 2 | no | — |
| 234 | C2×D4 | — | 268 | 1 | no | — |
| 235 | C2×D4 | — | 268 | 2 | no | — |
| 236 | C2×D4 | — | 268 | 2 | no | — |
| 237 | C2×D4 | — | 268 | 2 | no | — |
| 238 | C2×D4 | — | 268 | 2 | no | — |
| 239 | C2×D4 | — | 536 | 2 | no | — |
| 240 | C2×D4 | — | 67 | 4 | no | — |
| 241 | C2×D4 | — | 134 | 4 | no | — |
| 242 | C2×D4 | — | 134 | 2 | no | — |
| 243 | C2×D4 | — | 134 | 2 | no | — |
| 244 | C2×D4 | — | 134 | 2 | no | — |
| 245 | C2×D4 | — | 134 | 2 | no | — |
| 246 | C2×D4 | — | 134 | 2 | no | — |
| 247 | C2×D4 | — | 134 | 2 | no | — |
| 248 | C22×C4 | — | 2 | 2 | no | — |
| 249 | C22×C4 | — | 268 | 2 | no | — |
| 250 | C22×C4 | — | 268 | 2 | no | — |
| 251 | C22×C4 | — | 268 | 2 | no | — |
| 252 | C22×C4 | — | 268 | 2 | no | — |
| 253 | C22×C4 | — | 268 | 2 | no | — |
| 254 | C22×C4 | — | 268 | 2 | no | — |
| 255 | C22×C4 | — | 134 | 2 | no | — |
| 256 | C22×C4 | D4×D67 | 1 | 2 | yes | — |
| 257 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 258 | D8 | — | 268 | 16 | no | — |
| 259 | C2×C8 | — | 2 | 4 | no | — |
| 260 | C2×C8 | — | 4 | 2 | no | — |
| 261 | C2×C8 | — | 4 | 2 | no | — |
| 262 | C2×C8 | — | 268 | 1 | no | — |
| 263 | C2×C8 | — | 268 | 1 | no | — |
| 264 | C2×C8 | — | 134 | 2 | no | — |
| 265 | C4⋊C4 | — | 4 | 2 | no | — |
| 266 | C4⋊C4 | — | 4 | 2 | no | — |
| 267 | C4⋊C4 | — | 4 | 2 | no | — |
| 268 | C4⋊C4 | — | 134 | 2 | no | — |
| 269 | C4⋊C4 | — | 134 | 2 | no | — |
| 270 | C22⋊C4 | — | 268 | 8 | no | — |
| 271 | C22⋊C4 | — | 268 | 2 | no | — |
| 272 | C22⋊C4 | — | 268 | 2 | no | — |
| 273 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 274 | C42 | C2×D268 | 1 | 2 | yes | — |
| 275 | C42 | #11761629 | 1 | 1 | yes | characteristic |
| 276 | C23 | — | 268 | 2 | no | — |
| 277 | C23 | — | 268 | 2 | no | — |
| 278 | C23 | — | 268 | 2 | no | — |
| 279 | C23 | — | 268 | 2 | no | — |
| 280 | C23 | — | 268 | 2 | no | — |
| 281 | C23 | — | 268 | 2 | no | — |
| 282 | C23 | — | 268 | 2 | no | — |
| 283 | C23 | — | 536 | 2 | no | — |
| 284 | C23 | — | 536 | 2 | no | — |
| 285 | C23 | — | 536 | 1 | no | — |
| 286 | C23 | — | 536 | 1 | no | — |
| 287 | C23 | — | 134 | 4 | no | — |
| 288 | C23 | #14524013 | 1 | 1 | yes | characteristic |
| 289 | D4 | — | 268 | 4 | no | — |
| 290 | D4 | — | 268 | 4 | no | — |
| 291 | D4 | — | 268 | 2 | no | — |
| 292 | D4 | — | 268 | 4 | no | — |
| 293 | D4 | — | 268 | 2 | no | — |
| 294 | D4 | — | 536 | 2 | no | — |
| 295 | D4 | — | 536 | 8 | no | — |
| 296 | D4 | — | 536 | 2 | no | — |
| 297 | D4 | — | 536 | 2 | no | — |
| 298 | D4 | — | 134 | 4 | no | — |
| 299 | D4 | — | 134 | 4 | no | — |
| 300 | C2×C4 | — | 2 | 1 | no | — |
| 301 | C2×C4 | — | 2 | 1 | no | — |
| 302 | C2×C4 | — | 4 | 4 | no | — |
| 303 | C2×C4 | — | 4 | 2 | no | — |
| 304 | C2×C4 | — | 268 | 2 | no | — |
| 305 | C2×C4 | — | 268 | 2 | no | — |
| 306 | C2×C4 | — | 268 | 2 | no | — |
| 307 | C2×C4 | — | 536 | 2 | no | — |
| 308 | C2×C4 | — | 536 | 2 | no | — |
| 309 | C2×C4 | — | 536 | 2 | no | — |
| 310 | C2×C4 | — | 536 | 2 | no | — |
| 311 | C2×C4 | #14524013 | 1 | 2 | yes | — |
| 312 | C2×C4 | #14524018 | 1 | 1 | yes | characteristic |
| 313 | C2×C4 | #14524018 | 1 | 2 | yes | — |
| 314 | C2×C4 | #14524040 | 1 | 1 | yes | characteristic |
| 315 | C2×C4 | D8×D67 | 1 | 2 | yes | — |
| 316 | C2×C4 | #14524066 | 1 | 2 | yes | — |
| 317 | C2×C4 | #14524070 | 1 | 2 | yes | — |
| 318 | C2×C4 | #14524070 | 1 | 2 | yes | — |
| 319 | C8 | — | 4 | 4 | no | — |
| 320 | C8 | — | 268 | 2 | no | — |
| 321 | C22 | — | 268 | 4 | no | — |
| 322 | C22 | — | 268 | 4 | no | — |
| 323 | C22 | — | 268 | 4 | no | — |
| 324 | C22 | — | 536 | 2 | no | — |
| 325 | C22 | — | 536 | 2 | no | — |
| 326 | C22 | — | 536 | 2 | no | — |
| 327 | C22 | — | 536 | 2 | no | — |
| 328 | C22 | — | 536 | 4 | no | — |
| 329 | C22 | — | 536 | 2 | no | — |
| 330 | C22 | — | 1072 | 1 | no | — |
| 331 | C22 | — | 1072 | 1 | no | — |
| 332 | C22 | — | 1072 | 2 | no | — |
| 333 | C22 | #16863306 | 1 | 1 | yes | characteristic |
| 334 | C22 | #16863531 | 1 | 2 | yes | — |
| 335 | C22 | #16863544 | 1 | 2 | yes | — |
| 336 | C22 | #16863566 | 1 | 1 | yes | characteristic |
| 337 | C22 | #16863571 | 1 | 1 | yes | characteristic |
| 338 | C4 | — | 2 | 1 | no | — |
| 339 | C4 | — | 2 | 1 | no | — |
| 340 | C4 | — | 8 | 2 | no | — |
| 341 | C4 | — | 536 | 2 | no | — |
| 342 | C4 | #16863531 | 1 | 2 | yes | — |
| 343 | C4 | #16863544 | 1 | 2 | yes | — |
| 344 | C4 | #16863633 | 1 | 2 | yes | — |
| 345 | C4 | #16863650 | 1 | 2 | yes | — |
| 346 | C2 | — | 536 | 4 | no | — |
| 347 | C2 | — | 1072 | 2 | no | — |
| 348 | C2 | #22559264 | 1 | 1 | yes | characteristic |
| 349 | C2 | #22559293 | 1 | 1 | yes | characteristic |
| 350 | C2 | #22559299 | 1 | 2 | yes | — |
| 351 | C2 | #22561208 | 1 | 2 | yes | — |
| 352 | C2 | #22561253 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16863592 | C2 | semidirect |
| 2. #22565125 | C2 | semidirect |
| 3. #22561014 | C2 | semidirect |
| 4. C2×#16863123 | C2 | semidirect |
| 5. C67×#1296 | C2 | semidirect |
| 31. #14524040 | D4 | semidirect |
| 50. C4⋊C8×C67 | D4 | semidirect |
| 70. C2×D268 | D8 | semidirect |
| 181. #1296 | D67 | semidirect |
| 182. C67 | #10228 | semidirect |
| 223. C4⋊C8 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863592 | 2 |
| #22565125 | 2 |
| #22561014 | 2 |
| C2×#16863123 | 2 |
| C67×#1296 | 2 |
| #10228 | 67 |