Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
214 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 58 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. #63872 | C2 | semidirect |
| 3. C8×C3⋊Dic3 | C2 | semidirect |
| 5. C3×#816 | C2 | semidirect |
| 6. #63565 | C2 | semidirect |
| 30. #816 | D3 | semidirect |
| 166. C32 | #488 | semidirect |
| 203. C3 | #4768 | semidirect |
| 204. C3 | #4800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63872 | 2 |
| #63863 | 2 |
| C8×C3⋊Dic3 | 2 |
| C3×#821 | 2 |
| C3×#816 | 2 |
| #63565 | 2 |
| #63562 | 2 |
| #4800 | 3 |
| #4768 | 3 |