Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
326 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 326 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 |
|---|---|---|
| 4. C3×#824 | C2 | semidirect |
| 5. #63560 | C2 | semidirect |
| 29. #824 | D3 | semidirect |
| 117. C3⋊D3 | #101 | semidirect |
| 151. C32 | C2×#101 | semidirect |
| 187. C3 | D3×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3797 | 2 |
| M16×C3⋊D3 | 2 |
| #63818 | 2 |
| C3×#824 | 2 |
| #63560 | 2 |
| D3×#101 | 3 |