Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
4778 conjugacy classes of subgroups; only the 727 normal subgroups are shown.
This group has 4778 conjugacy classes of subgroups — too many to draw. Only its 727 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 | #22603152 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22601999 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22601995 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22597743 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #22597734 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #22596803 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C71×#2884 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #17986836 | — | 2 | 8 | no | — |
| 9 | #17986835 | — | 2 | 4 | no | — |
| 10 | #17986835 | C22 | 1 | 12 | yes | — |
| 11 | C2×#14556176 | — | 2 | 4 | no | — |
| 12 | C2×#14556176 | C22 | 1 | 2 | yes | — |
| 13 | 2−1+4×D71 | — | 2 | 8 | no | — |
| 14 | C22×#11765866 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #17986671 | — | 2 | 8 | no | — |
| 16 | #17986668 | — | 2 | 4 | no | — |
| 17 | #17986661 | — | 2 | 8 | no | — |
| 18 | #17986660 | — | 2 | 4 | no | — |
| 19 | #17986568 | C22 | 1 | 12 | yes | complemented |
| 20 | #17986563 | C22 | 1 | 6 | yes | complemented |
| 21 | #17986511 | C22 | 1 | 12 | yes | complemented |
| 22 | #17986506 | C22 | 1 | 6 | yes | complemented |
| 23 | #17986477 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #17986190 | C22 | 1 | 16 | yes | complemented |
| 25 | #17986187 | C22 | 1 | 48 | yes | complemented |
| 26 | #17985972 | C22 | 1 | 24 | yes | complemented |
| 27 | C2×2−1+4×C71 | C22 | 1 | 1 | yes | characteristic |
| 28 | #519×C71 | C22 | 1 | 2 | yes | complemented |
| 29 | #410×C71 | C22 | 1 | 12 | yes | complemented |
| 30 | #14556176 | — | 2 | 32 | no | — |
| 31 | #14556176 | — | 2 | 8 | no | — |
| 32 | #14556176 | — | 2 | 12 | no | — |
| 33 | #14556176 | — | 2 | 8 | no | — |
| 34 | #14556175 | — | 2 | 16 | no | — |
| 35 | #14556175 | — | 2 | 24 | no | — |
| 36 | #14556174 | — | 2 | 16 | no | — |
| 37 | #14556174 | — | 2 | 24 | no | — |
| 38 | #14556173 | — | 2 | 12 | no | — |
| 39 | #14556173 | C23 | 1 | 16 | yes | — |
| 40 | C2×#11765866 | — | 2 | 16 | no | — |
| 41 | C2×#11765866 | — | 2 | 4 | no | — |
| 42 | C2×#11765866 | — | 2 | 8 | no | — |
| 43 | C2×#11765866 | D4 | 1 | 8 | yes | complemented |
| 44 | C2×#11765865 | — | 2 | 24 | no | — |
| 45 | C2×#11765865 | C23 | 1 | 12 | yes | — |
| 46 | #41×D71 | — | 2 | 32 | no | — |
| 47 | #41×D71 | — | 2 | 48 | no | — |
| 48 | C2×Q8×D71 | — | 2 | 16 | no | — |
| 49 | C2×Q8×D71 | D4 | 1 | 8 | yes | complemented |
| 50 | C22×D284 | C23 | 1 | 3 | yes | — |
| 51 | C22×C4×D71 | C23 | 1 | 3 | yes | — |
| 52 | #14556125 | — | 2 | 12 | no | — |
| 53 | #14556124 | — | 2 | 6 | no | — |
| 54 | #14556117 | — | 2 | 6 | no | — |
| 55 | #14556116 | — | 2 | 12 | no | — |
| 56 | #14556112 | C23 | 1 | 8 | yes | — |
| 57 | #14556109 | C23 | 1 | 4 | yes | — |
| 58 | #14556108 | — | 2 | 12 | no | — |
| 59 | #14556104 | — | 2 | 6 | no | — |
| 60 | #14556103 | — | 2 | 12 | no | — |
| 61 | #14556103 | — | 2 | 24 | no | — |
| 62 | #14556102 | — | 2 | 12 | no | — |
| 63 | #14556099 | — | 2 | 6 | no | — |
| 64 | #14556098 | C23 | 1 | 24 | yes | — |
| 65 | #14556096 | C23 | 1 | 12 | yes | — |
| 66 | Q8×Dic71 | — | 2 | 4 | no | — |
| 67 | C4×D284 | — | 2 | 24 | no | — |
| 68 | C4×C22⋊D71 | — | 2 | 12 | no | — |
| 69 | #14556087 | C23 | 1 | 6 | yes | — |
| 70 | #14556042 | C23 | 1 | 32 | yes | — |
| 71 | 2−1+4×C71 | — | 2 | 8 | no | — |
| 72 | C2×#41×C71 | D4 | 1 | 4 | yes | complemented |
| 73 | C2×#41×C71 | C23 | 1 | 6 | yes | — |
| 74 | C22×Q8×C71 | D4 | 1 | 4 | yes | complemented |
| 75 | C22×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 76 | C4×Q8×C71 | — | 2 | 8 | no | — |
| 77 | #117×C71 | C23 | 1 | 12 | yes | — |
| 78 | #99×C71 | C23 | 1 | 16 | yes | — |
| 79 | C23×D71 | C24 | 1 | 3 | yes | — |
| 80 | #11765866 | — | 2 | 48 | no | — |
| 81 | #11765866 | — | 2 | 32 | no | — |
| 82 | #11765866 | — | 4 | 16 | no | — |
| 83 | #11765865 | — | 2 | 48 | no | — |
| 84 | #11765865 | — | 2 | 48 | no | — |
| 85 | #11765865 | — | 2 | 24 | no | — |
| 86 | #11765865 | — | 2 | 16 | no | — |
| 87 | #11765865 | — | 2 | 24 | no | — |
| 88 | #11765864 | — | 2 | 48 | no | — |
| 89 | #11765864 | — | 2 | 32 | no | — |
| 90 | C2×Dic142 | — | 2 | 24 | no | — |
| 91 | C2×Dic142 | C2×D4 | 1 | 12 | yes | — |
| 92 | Q8×D71 | — | 2 | 48 | no | — |
| 93 | Q8×D71 | — | 2 | 32 | no | — |
| 94 | C2×D284 | — | 2 | 24 | no | — |
| 95 | C2×D284 | — | 2 | 6 | no | — |
| 96 | C2×D284 | — | 2 | 12 | no | — |
| 97 | C2×D284 | — | 2 | 24 | no | — |
| 98 | C2×D284 | C2×D4 | 1 | 12 | yes | — |
| 99 | C2×C22⋊D71 | — | 2 | 16 | no | — |
| 100 | C2×C22⋊D71 | — | 2 | 12 | no | — |
| 101 | C2×C22⋊D71 | C24 | 1 | 8 | yes | — |
| 102 | D4×D71 | — | 2 | 48 | no | — |
| 103 | D4×D71 | — | 2 | 32 | no | — |
| 104 | C22×Dic71 | C24 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×D71 | — | 2 | 48 | no | — |
| 106 | C2×C4×D71 | — | 2 | 6 | no | — |
| 107 | C2×C4×D71 | — | 2 | 12 | no | — |
| 108 | C2×C4×D71 | C2×D4 | 1 | 24 | yes | — |
| 109 | C4⋊Dic71 | — | 2 | 6 | no | — |
| 110 | C4⋊Dic71 | — | 2 | 8 | no | — |
| 111 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 112 | C22⋊Dic71 | — | 2 | 4 | no | — |
| 113 | C22⋊Dic71 | C24 | 1 | 4 | yes | — |
| 114 | (C2×D71)⋊C4 | — | 2 | 8 | no | — |
| 115 | (C2×D71)⋊C4 | — | 2 | 12 | no | — |
| 116 | (C2×D71)⋊C4 | — | 2 | 24 | no | — |
| 117 | C4×Dic71 | — | 2 | 6 | no | — |
| 118 | #41×C71 | — | 2 | 16 | no | — |
| 119 | #41×C71 | — | 2 | 24 | no | — |
| 120 | C2×Q8×C71 | — | 2 | 16 | no | — |
| 121 | C2×Q8×C71 | C2×D4 | 1 | 8 | yes | — |
| 122 | C2×Q8×C71 | C2×D4 | 1 | 6 | yes | — |
| 123 | C2×Q8×C71 | C2×D4 | 1 | 4 | yes | — |
| 124 | C2×D4×C71 | C2×D4 | 1 | 6 | yes | — |
| 125 | C2×D4×C71 | C24 | 1 | 4 | yes | — |
| 126 | C22×C4×C71 | C2×D4 | 1 | 12 | yes | — |
| 127 | C22×C4×C71 | C24 | 1 | 3 | yes | — |
| 128 | C4⋊C4×C71 | — | 2 | 12 | no | — |
| 129 | C22⋊C4×C71 | C24 | 1 | 8 | yes | — |
| 130 | C42×C71 | — | 2 | 12 | no | — |
| 131 | C23×C71 | C22×D4 | 1 | 4 | yes | — |
| 132 | C23×C71 | C25 | 1 | 1 | yes | characteristic |
| 133 | C22×D71 | — | 2 | 16 | no | — |
| 134 | C22×D71 | — | 2 | 3 | no | — |
| 135 | C22×D71 | — | 2 | 6 | no | — |
| 136 | C22×D71 | — | 8 | 3 | no | — |
| 137 | C22×D71 | C22×D4 | 1 | 8 | yes | — |
| 138 | Q8×C71 | — | 2 | 12 | no | — |
| 139 | Q8×C71 | #120 | 1 | 16 | yes | — |
| 140 | D4×C71 | — | 2 | 8 | no | — |
| 141 | D4×C71 | — | 2 | 12 | no | — |
| 142 | C2×C4×C71 | — | 2 | 24 | no | — |
| 143 | C2×C4×C71 | — | 2 | 8 | no | — |
| 144 | C2×C4×C71 | C22×D4 | 1 | 12 | yes | — |
| 145 | C2×C4×C71 | C22×D4 | 1 | 4 | yes | — |
| 146 | C2×C4×C71 | C22×D4 | 1 | 6 | yes | — |
| 147 | C22⋊D71 | — | 2 | 32 | no | — |
| 148 | C22⋊D71 | — | 2 | 8 | no | — |
| 149 | C22⋊D71 | — | 2 | 8 | no | — |
| 150 | C22⋊D71 | — | 8 | 12 | no | — |
| 151 | C2×Dic71 | — | 2 | 16 | no | — |
| 152 | C2×Dic71 | — | 2 | 4 | no | — |
| 153 | C2×Dic71 | — | 2 | 2 | no | — |
| 154 | C2×Dic71 | — | 2 | 1 | no | — |
| 155 | C2×Dic71 | C22×D4 | 1 | 8 | yes | — |
| 156 | D284 | — | 2 | 16 | no | — |
| 157 | D284 | — | 2 | 24 | no | — |
| 158 | D284 | — | 4 | 12 | no | — |
| 159 | D284 | — | 8 | 24 | no | — |
| 160 | C4×D71 | — | 2 | 32 | no | — |
| 161 | C4×D71 | — | 2 | 48 | no | — |
| 162 | C4×D71 | — | 4 | 12 | no | — |
| 163 | Dic142 | — | 2 | 16 | no | — |
| 164 | Dic142 | — | 2 | 24 | no | — |
| 165 | C22×C71 | — | 2 | 4 | no | — |
| 166 | C22×C71 | — | 4 | 1 | no | — |
| 167 | C22×C71 | — | 4 | 4 | no | — |
| 168 | C22×C71 | C23×D4 | 1 | 2 | yes | — |
| 169 | C22×C71 | C23×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×D71 | — | 2 | 8 | no | — |
| 171 | C2×D71 | — | 4 | 8 | no | — |
| 172 | C2×D71 | — | 4 | 12 | no | — |
| 173 | C2×D71 | — | 4 | 6 | no | — |
| 174 | C2×D71 | — | 4 | 3 | no | — |
| 175 | C2×D71 | — | 8 | 16 | no | — |
| 176 | C4×C71 | — | 2 | 4 | no | — |
| 177 | C4×C71 | — | 4 | 8 | no | — |
| 178 | C4×C71 | C2×#120 | 1 | 12 | yes | — |
| 179 | Dic71 | — | 2 | 8 | no | — |
| 180 | Dic71 | — | 4 | 4 | no | — |
| 181 | Dic71 | — | 4 | 1 | no | — |
| 182 | #60402 | — | 71 | 1 | no | maximal, Sylow |
| 183 | C2×C71 | — | 2 | 1 | no | — |
| 184 | C2×C71 | — | 2 | 2 | no | — |
| 185 | C2×C71 | — | 4 | 4 | no | — |
| 186 | C2×C71 | C22×#120 | 1 | 1 | yes | characteristic |
| 187 | D71 | — | 4 | 8 | no | — |
| 188 | D71 | — | 8 | 3 | no | — |
| 189 | 2−1+6 | — | 71 | 1 | no | — |
| 190 | #3487 | — | 71 | 1 | no | — |
| 191 | #3487 | — | 71 | 2 | no | — |
| 192 | #3027 | — | 71 | 12 | no | — |
| 193 | #3025 | — | 71 | 12 | no | — |
| 194 | #2884 | — | 71 | 2 | no | — |
| 195 | #2884 | D71 | 1 | 1 | yes | characteristic, complemented |
| 196 | C71 | #60402 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 197 | #585 | — | 71 | 12 | no | — |
| 198 | #585 | — | 142 | 8 | no | — |
| 199 | #585 | — | 142 | 4 | no | — |
| 200 | C2×2−1+4 | — | 71 | 2 | no | — |
| 201 | C2×2−1+4 | — | 142 | 8 | no | — |
| 202 | C2×2−1+4 | — | 142 | 4 | no | — |
| 203 | C2×2−1+4 | C2×D71 | 1 | 1 | yes | characteristic |
| 204 | C22×#41 | — | 71 | 1 | no | — |
| 205 | #550 | — | 142 | 8 | no | — |
| 206 | #550 | — | 142 | 4 | no | — |
| 207 | #548 | — | 142 | 8 | no | — |
| 208 | #548 | — | 142 | 4 | no | — |
| 209 | #535 | — | 71 | 6 | no | — |
| 210 | #535 | — | 71 | 12 | no | — |
| 211 | #525 | — | 71 | 6 | no | — |
| 212 | #525 | — | 71 | 12 | no | — |
| 213 | #519 | — | 71 | 1 | no | — |
| 214 | #519 | C2×D71 | 1 | 2 | yes | complemented |
| 215 | #458 | — | 71 | 16 | no | — |
| 216 | B(4,𝔽2) | — | 71 | 48 | no | — |
| 217 | #410 | — | 71 | 24 | no | — |
| 218 | #410 | C2×D71 | 1 | 12 | yes | complemented |
| 219 | 2−1+4 | — | 2 | 8 | no | — |
| 220 | 2−1+4 | — | 142 | 32 | no | — |
| 221 | 2−1+4 | — | 142 | 24 | no | — |
| 222 | 2−1+4 | — | 142 | 16 | no | — |
| 223 | 2−1+4 | — | 142 | 8 | no | — |
| 224 | 2−1+4 | — | 142 | 8 | no | — |
| 225 | 2−1+4 | — | 142 | 12 | no | — |
| 226 | H(5,𝔽2) | — | 71 | 16 | no | — |
| 227 | H(5,𝔽2) | — | 142 | 24 | no | — |
| 228 | H(5,𝔽2) | — | 142 | 16 | no | — |
| 229 | H(5,𝔽2) | — | 142 | 12 | no | — |
| 230 | C2×#41 | — | 71 | 8 | no | — |
| 231 | C2×#41 | — | 71 | 12 | no | — |
| 232 | C2×#41 | — | 142 | 48 | no | — |
| 233 | C2×#41 | — | 142 | 16 | no | — |
| 234 | C2×#41 | — | 142 | 32 | no | — |
| 235 | C2×#41 | — | 142 | 8 | no | — |
| 236 | C2×#41 | — | 142 | 4 | no | — |
| 237 | C2×#41 | — | 142 | 24 | no | — |
| 238 | C2×#41 | D284 | 1 | 4 | yes | complemented |
| 239 | C2×#41 | C22×D71 | 1 | 6 | yes | — |
| 240 | C22×Q8 | — | 71 | 8 | no | — |
| 241 | C22×Q8 | — | 142 | 16 | no | — |
| 242 | C22×Q8 | D284 | 1 | 4 | yes | complemented |
| 243 | C22×Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 244 | C22×D4 | — | 71 | 3 | no | — |
| 245 | C23×C4 | — | 71 | 3 | no | — |
| 246 | #127 | — | 142 | 12 | no | — |
| 247 | #127 | — | 142 | 6 | no | — |
| 248 | #124 | — | 142 | 12 | no | — |
| 249 | #124 | — | 142 | 6 | no | — |
| 250 | #123 | — | 71 | 4 | no | — |
| 251 | #123 | — | 71 | 8 | no | — |
| 252 | C22⋊Q8 | — | 142 | 12 | no | — |
| 253 | C22⋊Q8 | — | 142 | 6 | no | — |
| 254 | #121 | — | 142 | 24 | no | — |
| 255 | #121 | — | 142 | 12 | no | — |
| 256 | #121 | — | 142 | 6 | no | — |
| 257 | #121 | — | 142 | 12 | no | — |
| 258 | #120 | — | 71 | 12 | no | — |
| 259 | #120 | — | 71 | 24 | no | — |
| 260 | C4×Q8 | — | 2 | 8 | no | — |
| 261 | C4×Q8 | — | 142 | 4 | no | — |
| 262 | C4×D4 | — | 142 | 24 | no | — |
| 263 | C4×D4 | — | 142 | 12 | no | — |
| 264 | #117 | — | 71 | 6 | no | — |
| 265 | #117 | C22×D71 | 1 | 12 | yes | — |
| 266 | #99 | — | 71 | 32 | no | — |
| 267 | #99 | C22×D71 | 1 | 16 | yes | — |
| 268 | C24 | — | 71 | 3 | no | — |
| 269 | #41 | — | 2 | 16 | no | — |
| 270 | #41 | — | 2 | 24 | no | — |
| 271 | #41 | — | 284 | 16 | no | — |
| 272 | #41 | — | 142 | 48 | no | — |
| 273 | #41 | — | 142 | 48 | no | — |
| 274 | #41 | — | 142 | 32 | no | — |
| 275 | #41 | — | 142 | 48 | no | — |
| 276 | #41 | — | 142 | 48 | no | — |
| 277 | #41 | — | 142 | 32 | no | — |
| 278 | #41 | — | 142 | 24 | no | — |
| 279 | #41 | — | 142 | 24 | no | — |
| 280 | #41 | — | 142 | 16 | no | — |
| 281 | C2×Q8 | — | 2 | 16 | no | — |
| 282 | C2×Q8 | — | 71 | 12 | no | — |
| 283 | C2×Q8 | — | 142 | 24 | no | — |
| 284 | C2×Q8 | — | 142 | 48 | no | — |
| 285 | C2×Q8 | — | 142 | 32 | no | — |
| 286 | C2×Q8 | D4×D71 | 1 | 8 | yes | — |
| 287 | C2×Q8 | C2×D284 | 1 | 6 | yes | — |
| 288 | C2×Q8 | C2×D284 | 1 | 4 | yes | — |
| 289 | C2×D4 | — | 71 | 8 | no | — |
| 290 | C2×D4 | — | 71 | 12 | no | — |
| 291 | C2×D4 | — | 142 | 24 | no | — |
| 292 | C2×D4 | — | 142 | 24 | no | — |
| 293 | C2×D4 | — | 142 | 32 | no | — |
| 294 | C2×D4 | — | 142 | 48 | no | — |
| 295 | C2×D4 | — | 142 | 12 | no | — |
| 296 | C2×D4 | — | 142 | 16 | no | — |
| 297 | C2×D4 | — | 142 | 12 | no | — |
| 298 | C2×D4 | — | 142 | 6 | no | — |
| 299 | C2×D4 | C2×D284 | 1 | 6 | yes | — |
| 300 | C2×D4 | C23×D71 | 1 | 4 | yes | — |
| 301 | C22×C4 | — | 71 | 24 | no | — |
| 302 | C22×C4 | — | 71 | 1 | no | — |
| 303 | C22×C4 | — | 142 | 48 | no | — |
| 304 | C22×C4 | — | 142 | 12 | no | — |
| 305 | C22×C4 | — | 142 | 6 | no | — |
| 306 | C22×C4 | C2×D284 | 1 | 12 | yes | — |
| 307 | C22×C4 | C23×D71 | 1 | 3 | yes | — |
| 308 | C4⋊C4 | — | 2 | 12 | no | — |
| 309 | C4⋊C4 | — | 142 | 8 | no | — |
| 310 | C4⋊C4 | — | 142 | 4 | no | — |
| 311 | C4⋊C4 | — | 142 | 6 | no | — |
| 312 | C22⋊C4 | — | 71 | 4 | no | — |
| 313 | C22⋊C4 | — | 142 | 24 | no | — |
| 314 | C22⋊C4 | — | 142 | 8 | no | — |
| 315 | C22⋊C4 | — | 142 | 4 | no | — |
| 316 | C22⋊C4 | — | 142 | 12 | no | — |
| 317 | C22⋊C4 | C23×D71 | 1 | 8 | yes | — |
| 318 | C42 | — | 2 | 12 | no | — |
| 319 | C42 | — | 142 | 6 | no | — |
| 320 | C23 | — | 568 | 3 | no | — |
| 321 | C23 | — | 71 | 8 | no | — |
| 322 | C23 | — | 142 | 16 | no | — |
| 323 | C23 | — | 142 | 6 | no | — |
| 324 | C23 | — | 142 | 3 | no | — |
| 325 | C23 | C22×D284 | 1 | 4 | yes | — |
| 326 | C23 | C24×D71 | 1 | 1 | yes | characteristic |
| 327 | Q8 | — | 2 | 12 | no | — |
| 328 | Q8 | — | 142 | 16 | no | — |
| 329 | Q8 | — | 142 | 24 | no | — |
| 330 | Q8 | #14556098 | 1 | 16 | yes | — |
| 331 | D4 | — | 2 | 8 | no | — |
| 332 | D4 | — | 2 | 12 | no | — |
| 333 | D4 | — | 284 | 12 | no | — |
| 334 | D4 | — | 568 | 24 | no | — |
| 335 | D4 | — | 568 | 12 | no | — |
| 336 | D4 | — | 142 | 16 | no | — |
| 337 | D4 | — | 142 | 32 | no | — |
| 338 | D4 | — | 142 | 8 | no | — |
| 339 | D4 | — | 142 | 8 | no | — |
| 340 | D4 | — | 142 | 24 | no | — |
| 341 | C2×C4 | — | 2 | 24 | no | — |
| 342 | C2×C4 | — | 2 | 8 | no | — |
| 343 | C2×C4 | — | 284 | 12 | no | — |
| 344 | C2×C4 | — | 71 | 8 | no | — |
| 345 | C2×C4 | — | 142 | 32 | no | — |
| 346 | C2×C4 | — | 142 | 2 | no | — |
| 347 | C2×C4 | — | 142 | 4 | no | — |
| 348 | C2×C4 | — | 142 | 1 | no | — |
| 349 | C2×C4 | — | 142 | 16 | no | — |
| 350 | C2×C4 | — | 142 | 48 | no | — |
| 351 | C2×C4 | C2×D4×D71 | 1 | 12 | yes | — |
| 352 | C2×C4 | C22×D284 | 1 | 4 | yes | — |
| 353 | C2×C4 | C22×D284 | 1 | 6 | yes | — |
| 354 | C22 | — | 2 | 4 | no | — |
| 355 | C22 | — | 4 | 1 | no | — |
| 356 | C22 | — | 4 | 4 | no | — |
| 357 | C22 | — | 284 | 8 | no | — |
| 358 | C22 | — | 284 | 12 | no | — |
| 359 | C22 | — | 284 | 6 | no | — |
| 360 | C22 | — | 284 | 3 | no | — |
| 361 | C22 | — | 568 | 16 | no | — |
| 362 | C22 | — | 142 | 8 | no | — |
| 363 | C22 | C22×D4×D71 | 1 | 2 | yes | — |
| 364 | C22 | C23×D284 | 1 | 1 | yes | characteristic |
| 365 | C4 | — | 2 | 4 | no | — |
| 366 | C4 | — | 4 | 8 | no | — |
| 367 | C4 | — | 284 | 4 | no | — |
| 368 | C4 | — | 284 | 1 | no | — |
| 369 | C4 | — | 142 | 8 | no | — |
| 370 | C4 | C2×#14556098 | 1 | 12 | yes | — |
| 371 | C2 | — | 2 | 2 | no | — |
| 372 | C2 | — | 2 | 1 | no | — |
| 373 | C2 | — | 4 | 4 | no | — |
| 374 | C2 | — | 284 | 8 | no | — |
| 375 | C2 | — | 568 | 3 | no | — |
| 376 | C2 | C22×#14556098 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22603152 | C2 | semidirect |
| 2. #22601999 | C2 | semidirect |
| 3. #22601995 | C2 | semidirect |
| 4. #22597743 | C2 | semidirect |
| 5. #22597734 | C2 | semidirect |
| 6. #22596803 | C2 | semidirect |
| 7. C71×#2884 | C2 | semidirect |
| 14. C22×#11765866 | C22 | semidirect |
| 19. #17986568 | C22 | semidirect |
| 20. #17986563 | C22 | semidirect |
| 21. #17986511 | C22 | semidirect |
| 22. #17986506 | C22 | semidirect |
| 23. #17986477 | C22 | semidirect |
| 24. #17986190 | C22 | semidirect |
| 25. #17986187 | C22 | semidirect |
| 26. #17985972 | C22 | semidirect |
| 28. #519×C71 | C22 | semidirect |
| 29. #410×C71 | C22 | semidirect |
| 43. C2×#11765866 | D4 | semidirect |
| 49. C2×Q8×D71 | D4 | semidirect |
| 72. C2×#41×C71 | D4 | semidirect |
| 74. C22×Q8×C71 | D4 | semidirect |
| 195. #2884 | D71 | semidirect |
| 196. C71 | #60402 | semidirect |
| 214. #519 | C2×D71 | semidirect |
| 218. #410 | C2×D71 | semidirect |
| 238. C2×#41 | D284 | semidirect |
| 242. C22×Q8 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22603152 | 2 |
| #22601999 | 2 |
| #22601995 | 2 |
| #22597743 | 2 |
| #22597734 | 2 |
| #22596803 | 2 |
| C71×#2884 | 2 |
| #60402 | 71 |