Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
483 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 483 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.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D32 |
| commutator, socle, cosocle | C22×C32 | C24 |
| Fitting | C22×C32×C4 | C22 |
| prime radical | #64139 | C2 |
| hypercenter | C22×C4 | D32 |
| hypocenter | C32 | #539 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#924 | C2 | semidirect |
| 3. C2×C3×Dic3⋊C4 | C2 | semidirect |
| 4. #63966 | C2 | semidirect |
| 5. #63952 | C2 | semidirect |
| 6. #63897 | C2 | semidirect |
| 7. #63888 | C2 | semidirect |
| 8. #63848 | C2 | semidirect |
| 9. #63845 | C2 | semidirect |
| 41. #924 | D3 | semidirect |
| 42. C2×Dic3⋊C4 | D3 | semidirect |
| 243. C32 | #539 | semidirect |
| 290. C3 | #5515 | semidirect |
| 291. C3 | #5645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64139 | 2 |
| C3×#924 | 2 |
| C2×C3×Dic3⋊C4 | 2 |
| #63966 | 2 |
| #63952 | 2 |
| #63897 | 2 |
| #63888 | 2 |
| #63848 | 2 |
| #63845 | 2 |
| #5645 | 3 |
| #5515 | 3 |