Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
347 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 347 conjugacy classes of subgroups — too many to draw. Only its 104 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. Dic3×Dic12 | C2 | semidirect |
| 4. #10589371 | C2 | semidirect |
| 5. C3×Dic3×C16 | C2 | semidirect |
| 6. #10589118 | C2 | semidirect |
| 19. C3×#800 | C4 | semidirect |
| 36. Dic3×C16 | D3 | semidirect |
| 46. C3×Dic12 | C2×C4 | semidirect |
| 52. C32×C16 | C2×C4 | semidirect |
| 81. #800 | Dic3 | direct (N × H) |
| 134. Dic12 | C2×Dic3 | semidirect |
| 139. C3×C16 | C4×D3 | semidirect |
| 140. C3×C16 | C2×Dic3 | semidirect |
| 152. C3×Dic3 | SD32 | semidirect |
| 220. C16 | D3×Dic3 | semidirect |
| 247. Dic3 | #800 | direct (N × H) |
| 248. C32 | C4×SD32 | semidirect |
| 287. C3 | C4×#800 | semidirect |
| 288. C3 | Dic3×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#800 | 2 |
| Dic3×Dic12 | 2 |
| Dic3×D24 | 2 |
| #10589371 | 2 |
| C3×Dic3×C16 | 2 |
| #10589118 | 2 |
| #10589115 | 2 |
| Dic3×SD32 | 3 |
| C4×#800 | 3 |