Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
401 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 401 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10592387 | C2 | semidirect |
| 2. C3×#4694 | C2 | semidirect |
| 4. #10590300 | C2 | semidirect |
| 5. C3×#4458 | C2 | semidirect |
| 6. #10589095 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 30. #4694 | D3 | semidirect |
| 39. #4458 | D3 | semidirect |
| 314. C32 | #1697 | semidirect |
| 366. C3 | #68584 | semidirect |
| 367. C3 | #71202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592387 | 2 |
| C3×#4694 | 2 |
| #10590355 | 2 |
| #10590300 | 2 |
| C3×#4458 | 2 |
| #10589095 | 2 |
| #10589090 | 2 |
| #71202 | 3 |
| #68584 | 3 |