Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
594 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 139 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. #10592542 | C2 | semidirect |
| 2. #10592394 | C2 | semidirect |
| 3. #10592387 | C2 | semidirect |
| 4. C32×#334 | C2 | semidirect |
| 5. #10589351 | C2 | semidirect |
| 21. C3×#334 | D3 | semidirect |
| 67. C32×C8 | D8 | semidirect |
| 72. #334 | C3⋊D3 | semidirect |
| 129. C3×C8 | D24 | semidirect |
| 164. C32 | #1687 | semidirect |
| 182. C8 | #3745 | semidirect |
| 200. C3 | #68540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592542 | 2 |
| #10592394 | 2 |
| #10592387 | 2 |
| C32×#334 | 2 |
| #10589351 | 2 |
| #68540 | 3 |