Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
274 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 72 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. C3×#830 | C2 | semidirect |
| 4. #63575 | C2 | semidirect |
| 5. #63563 | C2 | semidirect |
| 24. #830 | D3 | semidirect |
| 149. C32 | #480 | semidirect |
| 187. C3 | #4736 | semidirect |
| 188. C3 | #5033 | 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 |
| C3×#930 | 2 |
| C3×#830 | 2 |
| #63575 | 2 |
| #63563 | 2 |
| #5033 | 3 |
| #4736 | 3 |