Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
215 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 215 conjugacy classes of subgroups — too many to draw. Only its 60 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. #63646 | C2 | semidirect |
| 5. #63560 | C2 | semidirect |
| 23. C2×Dic12 | D3 | semidirect |
| 135. C32 | #473 | semidirect |
| 163. C3 | #5143 | semidirect |
| 164. C3 | #5192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| C3×#901 | 2 |
| #63827 | 2 |
| #63646 | 2 |
| #63560 | 2 |
| #5192 | 3 |
| #5143 | 3 |