Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
357 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 94 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. Dic3×Dic12 | C2 | semidirect |
| 5. C3×#4503 | C2 | semidirect |
| 6. C3×Dic3×C16 | C2 | semidirect |
| 7. #10589141 | C2 | semidirect |
| 21. #63549 | C4 | semidirect |
| 34. #4503 | D3 | semidirect |
| 35. Dic3×C16 | D3 | semidirect |
| 48. C3×Dic12 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 132. Dic12 | C4×D3 | semidirect |
| 143. C3⋊C16 | C4×D3 | semidirect |
| 154. C3×Dic3 | SD32 | semidirect |
| 253. Dic3 | #800 | semidirect |
| 254. C32 | C4×SD32 | semidirect |
| 294. C3 | C4×#800 | semidirect |
| 295. C3 | #69206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3×Dic12 | 2 |
| #10590763 | 2 |
| C2×#63549 | 2 |
| #10589375 | 2 |
| C3×#4503 | 2 |
| C3×Dic3×C16 | 2 |
| #10589141 | 2 |
| #69206 | 3 |
| C4×#800 | 3 |