Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
307 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 307 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. #64147 | C2 | semidirect |
| 2. C2×C3×#213 | C2 | semidirect |
| 3. #63916 | C2 | semidirect |
| 4. C2×#3712 | C2 | semidirect |
| 5. C3×#832 | C2 | semidirect |
| 6. #63573 | C2 | semidirect |
| 7. #63563 | C2 | semidirect |
| 28. C2×#213 | D3 | semidirect |
| 34. #832 | D3 | semidirect |
| 54. C3×C3⋊C8 | D4 | semidirect |
| 152. C3⋊C8 | #67 | semidirect |
| 213. C32 | #469 | semidirect |
| 264. C3 | #4782 | semidirect |
| 265. C3 | #5159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64147 | 2 |
| C2×C3×#213 | 2 |
| #63916 | 2 |
| C2×#3712 | 2 |
| C3×#832 | 2 |
| #63573 | 2 |
| #63563 | 2 |
| #5159 | 3 |
| #4782 | 3 |