Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
319 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. D3×#208 | C2 | semidirect |
| 3. #63663 | C2 | semidirect |
| 4. C3×#836 | C2 | semidirect |
| 5. #63558 | C2 | semidirect |
| 27. #836 | D3 | semidirect |
| 151. C32 | #413 | semidirect |
| 186. C3 | #4751 | semidirect |
| 187. C3 | #5237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#239 | 2 |
| D3×#208 | 2 |
| #63663 | 2 |
| C3×#836 | 2 |
| #63558 | 2 |
| #5237 | 3 |
| #4751 | 3 |