Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1002 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 246 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. C22×D72 | C2 | semidirect |
| 2. C22×#3664 | C2 | semidirect |
| 3. C2×#63437 | C2 | semidirect |
| 4. C2×#63436 | C2 | semidirect |
| 5. C2×C9×#97 | C2 | semidirect |
| 6. #10588393 | C2 | direct (N × H) |
| 16. C2×D72 | C22 | semidirect |
| 18. C2×#3664 | C22 | semidirect |
| 20. #63437 | C22 | semidirect |
| 22. #63436 | C22 | semidirect |
| 23. C9×#97 | C22 | semidirect |
| 47. C2×C8×C9 | D4 | semidirect |
| 93. C8×C9 | C2×D4 | semidirect |
| 99. C2×#97 | D9 | semidirect |
| 152. #97 | C2×D9 | semidirect |
| 176. C2×C9 | #496 | semidirect |
| 200. C2×C8 | D36 | semidirect |
| 218. C9 | C2×#496 | semidirect |
| 241. C8 | C2×D36 | semidirect |
| 263. C2 | #10588393 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D72 | 2 |
| C22×#3664 | 2 |
| C2×#63437 | 2 |
| C2×#63436 | 2 |
| C2×C9×#97 | 2 |
| #10588393 | 2 |
| C2×#4712 | 3 |