Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
287 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 287 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×C4×Dic6 | C2 | semidirect |
| 4. C3×#803 | C2 | semidirect |
| 5. #63575 | C2 | semidirect |
| 6. #63566 | C2 | semidirect |
| 21. #3717 | C4 | semidirect |
| 28. C4×Dic6 | D3 | semidirect |
| 36. #803 | D3 | semidirect |
| 48. C3×Dic6 | C2×C4 | semidirect |
| 50. C3×C3⋊C8 | C2×C4 | semidirect |
| 130. Dic6 | C4×D3 | semidirect |
| 134. C3⋊C8 | C4×D3 | semidirect |
| 182. C32 | #440 | semidirect |
| 221. C3 | #4710 | semidirect |
| 222. C3 | #5026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊D3) | 2 |
| C3×C4×Dic6 | 2 |
| C2×#3717 | 2 |
| C3×#803 | 2 |
| #63575 | 2 |
| #63566 | 2 |
| #63564 | 2 |
| #5026 | 3 |
| #4710 | 3 |