Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
265 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 74 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×Dic6 | C2 | semidirect |
| 5. C3×#816 | C2 | semidirect |
| 6. C3×#815 | C2 | semidirect |
| 7. #63575 | C2 | semidirect |
| 21. #3717 | C4 | semidirect |
| 34. #816 | D3 | semidirect |
| 35. #815 | D3 | semidirect |
| 47. C3×Dic6 | C2×C4 | semidirect |
| 50. C3×C3⋊C8 | C2×C4 | semidirect |
| 125. Dic6 | C4×D3 | semidirect |
| 130. C3⋊C8 | C4×D3 | semidirect |
| 176. C32 | #440 | semidirect |
| 215. C3 | #4710 | semidirect |
| 216. C3 | #4817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63894 | 2 |
| Dic3×Dic6 | 2 |
| C2×#3717 | 2 |
| #63648 | 2 |
| C3×#816 | 2 |
| C3×#815 | 2 |
| #63575 | 2 |
| #4817 | 3 |
| #4710 | 3 |