Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
552 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 552 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. #10592547 | C2 | semidirect |
| 3. #10592378 | C2 | semidirect |
| 4. C32×#334 | C2 | semidirect |
| 5. #10589351 | C2 | semidirect |
| 21. C3×#334 | D3 | semidirect |
| 64. C32×C8 | SD16 | semidirect |
| 69. #334 | C3⋊D3 | semidirect |
| 121. C3×C8 | #204 | semidirect |
| 152. C32 | #1688 | semidirect |
| 168. C8 | #3744 | semidirect |
| 183. C3 | #68550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592547 | 2 |
| #10592394 | 2 |
| #10592378 | 2 |
| C32×#334 | 2 |
| #10589351 | 2 |
| #68550 | 3 |