Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
278 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 278 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 |
|---|---|---|
| 1. C2×#3746 | C2 | semidirect |
| 3. #63866 | C2 | semidirect |
| 5. C2×#3719 | C2 | semidirect |
| 7. C3×#815 | C2 | semidirect |
| 37. #815 | D3 | semidirect |
| 180. C32 | #497 | semidirect |
| 215. C3 | #4715 | semidirect |
| 216. C3 | #5167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3746 | 2 |
| C2×C3×#204 | 2 |
| #63866 | 2 |
| #63860 | 2 |
| C2×#3719 | 2 |
| C2×#3716 | 2 |
| C3×#815 | 2 |
| #5167 | 3 |
| #4715 | 3 |