Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
282 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 62 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×#3755 | C2 | semidirect |
| 2. C3×#947 | C2 | semidirect |
| 3. #63894 | C2 | semidirect |
| 5. C3×#835 | C2 | semidirect |
| 6. Dic3⋊(C3⋊C8) | C2 | semidirect |
| 7. #63562 | C2 | semidirect |
| 24. #947 | D3 | semidirect |
| 33. #835 | D3 | semidirect |
| 196. C32 | #463 | semidirect |
| 241. C3 | #4819 | semidirect |
| 242. C3 | #5057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3755 | 2 |
| C3×#947 | 2 |
| #63894 | 2 |
| C2×#3714 | 2 |
| C3×#835 | 2 |
| Dic3⋊(C3⋊C8) | 2 |
| #63562 | 2 |
| #5057 | 3 |
| #4819 | 3 |