Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
286 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 62 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. #64145 | C2 | semidirect |
| 3. #63898 | C2 | semidirect |
| 4. C2×#3716 | C2 | semidirect |
| 5. C3×#832 | C2 | semidirect |
| 6. #63572 | C2 | semidirect |
| 7. #63567 | C2 | semidirect |
| 33. #832 | D3 | semidirect |
| 200. C32 | #463 | semidirect |
| 245. C3 | #4787 | semidirect |
| 246. C3 | #5153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64145 | 2 |
| C2×C3×#213 | 2 |
| #63898 | 2 |
| C2×#3716 | 2 |
| C3×#832 | 2 |
| #63572 | 2 |
| #63567 | 2 |
| #5153 | 3 |
| #4787 | 3 |