Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
198 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 152. C32 | #479 | semidirect |
| 183. C3 | #4799 | semidirect |
| 184. C3 | #4829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63869 | 2 |
| Dic3×Dic6 | 2 |
| #63644 | 2 |
| C3×#816 | 2 |
| C3×Dic3⋊C8 | 2 |
| #63575 | 2 |
| #63566 | 2 |
| #4829 | 3 |
| #4799 | 3 |