Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
238 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 68 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×Dic12 | C2 | semidirect |
| 4. #63644 | C2 | semidirect |
| 5. #63566 | C2 | semidirect |
| 21. C2×Dic12 | D3 | semidirect |
| 130. C32 | #470 | semidirect |
| 159. C3 | #5137 | semidirect |
| 160. C3 | #5189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| #63856 | 2 |
| #63644 | 2 |
| #63566 | 2 |
| #5189 | 3 |
| #5137 | 3 |