Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
286 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 286 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×C3×D24 | C2 | semidirect |
| 2. C2×C3×D3×C8 | C2 | semidirect |
| 3. #63908 | C2 | semidirect |
| 4. #63645 | C2 | semidirect |
| 5. #63563 | C2 | semidirect |
| 21. C2×D24 | D3 | semidirect |
| 22. C2×D3×C8 | D3 | semidirect |
| 38. C32×C8 | D4 | semidirect |
| 67. C2×C3×D3 | D8 | semidirect |
| 101. C3×C8 | #67 | semidirect |
| 102. C3×C8 | #67 | semidirect |
| 132. C2×D3 | D24 | semidirect |
| 144. C32 | #466 | semidirect |
| 156. C8 | #625 | semidirect |
| 182. C3 | #5115 | semidirect |
| 183. C3 | #5157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D24 | 2 |
| C2×C3×D3×C8 | 2 |
| #63908 | 2 |
| #63645 | 2 |
| #63563 | 2 |
| #5157 | 3 |
| #5115 | 3 |