Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
258 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 258 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 |
| 4. C3×#818 | C2 | semidirect |
| 5. #63567 | C2 | semidirect |
| 25. #818 | D3 | semidirect |
| 64. C2×C3×D3 | Q16 | semidirect |
| 123. C2×D3 | Dic12 | semidirect |
| 137. C32 | #467 | semidirect |
| 170. C3 | #4887 | semidirect |
| 171. C3 | #5116 | 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×D3×C8 | 2 |
| #63857 | 2 |
| C3×#818 | 2 |
| #63567 | 2 |
| #5116 | 3 |
| #4887 | 3 |