Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
224 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×C3×Dic24 | C2 | semidirect |
| 3. C32×M64 | C2 | semidirect |
| 4. C3×Dic48 | C2 | semidirect |
| 5. C3×#4449 | C2 | semidirect |
| 7. #69374 | C3 | direct (N × H) |
| 19. C2×Dic24 | C2×C3 | semidirect |
| 24. C3×M64 | D3 | semidirect |
| 25. C3×M64 | C2×C3 | semidirect |
| 26. Dic48 | C2×C3 | semidirect |
| 27. #4449 | C2×C3 | semidirect |
| 73. M64 | C3×D3 | semidirect |
| 163. C32 | #2264 | semidirect |
| 189. C3 | #69374 | direct (N × H) |
| 190. C3 | C3×#2264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic24 | 2 |
| C3×#4904 | 2 |
| C32×M64 | 2 |
| C3×Dic48 | 2 |
| C3×#4449 | 2 |
| C3×#2264 | 3 |
| #69374 | 3 |