Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
370 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 2. C2×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C2×C3×#208 | C2 | semidirect |
| 4. #63566 | C2 | semidirect |
| 5. #63563 | C2 | semidirect |
| 12. C3×#235 | C4 | semidirect |
| 26. C2×#208 | D3 | semidirect |
| 42. C3×D12 | C2×C4 | semidirect |
| 45. C3×Dic6 | C2×C4 | semidirect |
| 62. #235 | Dic3 | semidirect |
| 126. D12 | C2×Dic3 | semidirect |
| 129. Dic6 | C2×Dic3 | semidirect |
| 181. C32 | #417 | semidirect |
| 225. C3 | #5133 | semidirect |
| 226. C3 | #5232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#235 | 2 |
| C2×C4⋊(C3⋊Dic3) | 2 |
| C2×C3×#208 | 2 |
| #63566 | 2 |
| #63563 | 2 |
| #5232 | 3 |
| #5133 | 3 |