Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
684 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 177 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. C32×#424 | C2 | semidirect |
| 4. C2×#63646 | C2 | semidirect |
| 6. #10592694 | C2 | semidirect |
| 7. #10589420 | C2 | semidirect |
| 24. C3×#424 | D3 | semidirect |
| 100. #424 | C3⋊D3 | semidirect |
| 238. C32 | #2063 | semidirect |
| 286. C3 | #70542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#424 | 2 |
| C2×#63650 | 2 |
| C2×#63648 | 2 |
| C2×#63646 | 2 |
| #10592700 | 2 |
| #10592694 | 2 |
| #10589420 | 2 |
| #70542 | 3 |