Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
381 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 381 conjugacy classes of subgroups — too many to draw. Only its 84 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×#800 | C2 | semidirect |
| 3. Dic3×Dic12 | C2 | semidirect |
| 4. C2×#63549 | C2 | semidirect |
| 5. #10589375 | C2 | semidirect |
| 6. C3×Dic3⋊C16 | C2 | semidirect |
| 7. #10589115 | C2 | semidirect |
| 28. C2×#800 | D3 | semidirect |
| 37. Dic3⋊C16 | D3 | semidirect |
| 50. C3×Dic12 | D4 | semidirect |
| 144. Dic12 | #67 | semidirect |
| 171. C3×Dic3 | SD32 | semidirect |
| 285. Dic3 | #800 | semidirect |
| 286. C32 | #2207 | semidirect |
| 333. C3 | #69292 | semidirect |
| 334. C3 | #71475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#800 | 2 |
| #10590880 | 2 |
| Dic3×Dic12 | 2 |
| C2×#63549 | 2 |
| #10589375 | 2 |
| C3×Dic3⋊C16 | 2 |
| #10589115 | 2 |
| #71475 | 3 |
| #69292 | 3 |