Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
249 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
| 3. Dic3×Dic6 | C2 | semidirect |
| 6. C3×Dic3⋊C8 | C2 | semidirect |
| 7. #63566 | C2 | semidirect |
| 27. C2×Dic12 | D3 | semidirect |
| 37. Dic3⋊C8 | D3 | semidirect |
| 183. C32 | #464 | semidirect |
| 223. C3 | #4845 | semidirect |
| 224. C3 | #5185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| #63864 | 2 |
| Dic3×Dic6 | 2 |
| C2×#3717 | 2 |
| #63648 | 2 |
| C3×Dic3⋊C8 | 2 |
| #63566 | 2 |
| #5185 | 3 |
| #4845 | 3 |