Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
371 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 88 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. C8×#634 | C2 | semidirect |
| 4. #10590284 | C2 | semidirect |
| 5. C3×#4457 | C2 | semidirect |
| 6. #10589095 | C2 | semidirect |
| 39. #4457 | D3 | semidirect |
| 292. C32 | #1678 | semidirect |
| 337. C3 | #68548 | semidirect |
| 338. C3 | #71208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#634 | 2 |
| C3×#4694 | 2 |
| #10590377 | 2 |
| #10590284 | 2 |
| C3×#4457 | 2 |
| #10589095 | 2 |
| #10589090 | 2 |
| #71208 | 3 |
| #68548 | 3 |