Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
792 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 3. C2×#63649 | C2 | semidirect |
| 5. C2×#63634 | C2 | semidirect |
| 6. C32×#343 | C2 | semidirect |
| 7. #10589420 | C2 | semidirect |
| 17. #64116 | C4 | semidirect |
| 32. C3×#343 | D3 | semidirect |
| 115. #343 | C3⋊D3 | semidirect |
| 256. C32 | #1816 | semidirect |
| 304. C3 | #69001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64116 | 2 |
| #10592832 | 2 |
| C2×#63649 | 2 |
| #10592665 | 2 |
| C2×#63634 | 2 |
| C32×#343 | 2 |
| #10589420 | 2 |
| #69001 | 3 |