Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
295 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 295 conjugacy classes of subgroups — too many to draw. Only its 66 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. D4×C3⋊Dic3 | C2 | semidirect |
| 2. C2×C3×#214 | C2 | semidirect |
| 4. #63863 | C2 | semidirect |
| 5. #63572 | C2 | semidirect |
| 6. #63566 | C2 | semidirect |
| 7. #63563 | C2 | semidirect |
| 30. C2×#214 | D3 | semidirect |
| 199. C32 | #463 | semidirect |
| 244. C3 | #5153 | semidirect |
| 245. C3 | #5165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C3⋊Dic3 | 2 |
| C2×C3×#214 | 2 |
| C2×C3×#213 | 2 |
| #63863 | 2 |
| #63572 | 2 |
| #63566 | 2 |
| #63563 | 2 |
| #5165 | 3 |
| #5153 | 3 |