Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
474 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 3. #63658 | C2 | semidirect |
| 4. C3×C3⋊#95 | C2 | semidirect |
| 5. #63579 | C2 | semidirect |
| 14. C2×C3×C4×D3 | C4 | semidirect |
| 26. C3⋊#95 | D3 | semidirect |
| 60. C2×C4×D3 | Dic3 | semidirect |
| 171. C32 | #381 | semidirect |
| 221. C3 | #4664 | semidirect |
| 222. C3 | #5211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×D3 | 2 |
| C2×(C2×D3)⋊Dic3 | 2 |
| #63658 | 2 |
| C3×C3⋊#95 | 2 |
| #63579 | 2 |
| #5211 | 3 |
| #4664 | 3 |