Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22601474 | C2 | semidirect |
| 2. #22598056 | C2 | semidirect |
| 3. #22598003 | C2 | semidirect |
| 4. #22590069 | C2 | semidirect |
| 5. #22589969 | C2 | semidirect |
| 6. #22586438 | C2 | semidirect |
| 7. C2×#360×C71 | C2 | semidirect |
| 66. C2×C71⋊C16 | D4 | semidirect |
| 68. #14556064 | D4 | semidirect |
| 78. C2×Q16×C71 | D4 | semidirect |
| 80. C2×D8×C71 | D4 | semidirect |
| 230. C2×#360 | D71 | semidirect |
| 234. C71 | #13318 | semidirect |
| 277. C2×Q16 | D284 | semidirect |
| 281. C2×D8 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| #22598056 | 2 |
| #22598003 | 2 |
| #22590069 | 2 |
| #22589969 | 2 |
| #22586438 | 2 |
| C2×#360×C71 | 2 |
| #13318 | 71 |