Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
434 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 1. C2×C4×C3⋊Dic3 | C2 | semidirect |
| 3. C2×C3×Dic3⋊C4 | C2 | semidirect |
| 6. #63579 | C2 | semidirect |
| 7. #63579 | C2 | semidirect |
| 21. (C2×D3)⋊Dic3 | C4 | semidirect |
| 29. C2×Dic3⋊C4 | D3 | semidirect |
| 251. C32 | #388 | semidirect |
| 322. C3 | #4945 | semidirect |
| 323. C3 | #4990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊Dic3 | 2 |
| C2×C3×(C2×D3)⋊C4 | 2 |
| C2×C3×Dic3⋊C4 | 2 |
| C2×(C2×D3)⋊Dic3 | 2 |
| #63579 | 2 |
| #4990 | 3 |
| #4945 | 3 |