Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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. #63843 | C2 | semidirect |
| 4. #63642 | C2 | semidirect |
| 6. C3×#816 | C2 | semidirect |
| 7. #63576 | C2 | semidirect |
| 21. #3715 | C4 | semidirect |
| 31. #816 | D3 | semidirect |
| 47. C3×Dic6 | C2×C4 | semidirect |
| 50. C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 123. Dic6 | C4×D3 | semidirect |
| 173. C32 | #440 | semidirect |
| 211. C3 | #4757 | semidirect |
| 212. C3 | #4817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63898 | 2 |
| #63843 | 2 |
| C2×#3715 | 2 |
| #63642 | 2 |
| C3×#821 | 2 |
| C3×#816 | 2 |
| #63576 | 2 |
| #4817 | 3 |
| #4757 | 3 |