Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22598056 | C2 | semidirect |
| 2. #22597998 | C2 | semidirect |
| 3. C2×#17985809 | C2 | semidirect |
| 4. #22590068 | C2 | semidirect |
| 5. #22589967 | C2 | semidirect |
| 6. #22586439 | C2 | semidirect |
| 7. C71×#3414 | C2 | semidirect |
| 57. #14556064 | D4 | semidirect |
| 75. C2×Q16×C71 | D4 | semidirect |
| 79. C2×D8×C71 | D4 | semidirect |
| 87. C2×C16×C71 | D4 | semidirect |
| 227. #3414 | D71 | semidirect |
| 234. C71 | #13318 | semidirect |
| 277. C2×Q16 | C22⋊D71 | semidirect |
| 281. C2×D8 | C22⋊D71 | semidirect |
| 306. C2×C16 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598056 | 2 |
| #22597998 | 2 |
| C2×#17985809 | 2 |
| #22590068 | 2 |
| #22589967 | 2 |
| #22586439 | 2 |
| C71×#3414 | 2 |
| #13318 | 71 |