Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
278 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 278 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. C3×#895 | C2 | semidirect |
| 2. #63908 | C2 | semidirect |
| 3. C2×#3713 | C2 | semidirect |
| 4. C2×#3711 | C2 | semidirect |
| 5. #63635 | C2 | semidirect |
| 6. C3×#809 | C2 | semidirect |
| 7. #63563 | C2 | semidirect |
| 30. #895 | D3 | semidirect |
| 34. #809 | D3 | semidirect |
| 53. C3⋊(C3⋊C8) | D4 | semidirect |
| 199. C32 | #469 | semidirect |
| 248. C3 | #4782 | semidirect |
| 249. C3 | #5039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#895 | 2 |
| #63908 | 2 |
| C2×#3713 | 2 |
| C2×#3711 | 2 |
| #63635 | 2 |
| C3×#809 | 2 |
| #63563 | 2 |
| #5039 | 3 |
| #4782 | 3 |