Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
972 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 261 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 |
|---|---|---|
| 4. #10592820 | C2 | semidirect |
| 5. #10589421 | C2 | semidirect |
| 16. C32×#100 | C4 | semidirect |
| 35. C32×M16 | C2×C4 | semidirect |
| 55. C3×#100 | Dic3 | semidirect |
| 96. C3×M16 | C2×Dic3 | semidirect |
| 133. #100 | C3⋊Dic3 | semidirect |
| 173. M16 | C2×C3⋊Dic3 | semidirect |
| 199. C32 | #1856 | semidirect |
| 244. C3 | #70068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596269 | 2 |
| C2×C32×#100 | 2 |
| #10592920 | 2 |
| #10592820 | 2 |
| #10589421 | 2 |
| #70068 | 3 |