Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
217 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 217 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 163. C32 | #487 | semidirect |
| 197. C3 | #4681 | semidirect |
| 198. C3 | #4792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63918 | 2 |
| #63866 | 2 |
| #63643 | 2 |
| C3×#816 | 2 |
| C3×C8×Dic3 | 2 |
| #63567 | 2 |
| #63566 | 2 |
| #4792 | 3 |
| #4681 | 3 |