Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
321 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 4. #63643 | C2 | semidirect |
| 5. C3×#816 | C2 | semidirect |
| 6. #63567 | C2 | semidirect |
| 7. #63566 | C2 | semidirect |
| 16. D3×Dic6 | C4 | semidirect |
| 37. #816 | D3 | semidirect |
| 191. C32 | #419 | semidirect |
| 232. C3 | #4802 | semidirect |
| 233. C3 | #5120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Dic6 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| #63841 | 2 |
| #63643 | 2 |
| C3×#816 | 2 |
| #63567 | 2 |
| #63566 | 2 |
| #5120 | 3 |
| #4802 | 3 |