Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
822 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 215 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×#382 | C2 | semidirect |
| 4. C2×#63635 | C2 | semidirect |
| 5. C2×#63634 | C2 | semidirect |
| 7. #10589390 | C2 | semidirect |
| 22. C3×#382 | D3 | semidirect |
| 102. #382 | C3⋊D3 | semidirect |
| 240. C32 | #2092 | semidirect |
| 292. C3 | #69558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#382 | 2 |
| C2×#63636 | 2 |
| C2×#63635 | 2 |
| C2×#63634 | 2 |
| #10592638 | 2 |
| #10589390 | 2 |
| #69558 | 3 |