Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10592399 | C2 | semidirect |
| 2. C3×#4695 | C2 | semidirect |
| 3. #10590633 | C2 | semidirect |
| 4. C3×#4463 | C2 | semidirect |
| 5. #10589127 | C2 | semidirect |
| 25. #4695 | D3 | semidirect |
| 29. #4463 | D3 | semidirect |
| 37. #3746 | D4 | semidirect |
| 38. #3745 | D4 | semidirect |
| 242. C32 | #2213 | semidirect |
| 278. C3 | #69305 | semidirect |
| 279. C3 | #71295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592399 | 2 |
| C3×#4695 | 2 |
| #10590633 | 2 |
| C3×#4463 | 2 |
| #10589127 | 2 |
| #71295 | 3 |
| #69305 | 3 |