Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
249 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 2. C32×C4×C16 | C2 | semidirect |
| 3. C3×#4458 | C2 | semidirect |
| 5. #67504 | C3 | direct (N × H) |
| 16. C3×C4×C16 | D3 | semidirect |
| 17. C3×C4×C16 | C2×C3 | semidirect |
| 19. #4458 | C2×C3 | semidirect |
| 29. C3×D24 | C8 | semidirect |
| 62. C4×C16 | C3×D3 | semidirect |
| 86. D24 | C3×C8 | semidirect |
| 180. C32 | #1331 | semidirect |
| 216. C3 | #67504 | direct (N × H) |
| 217. C3 | C3×#1331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D24 | 2 |
| C32×C4×C16 | 2 |
| C3×#4458 | 2 |
| C3×#1331 | 3 |
| #67504 | 3 |