Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
670 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 200 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 | C2×C32 | C23×C4 |
| Fitting | C2×C32×D4 | C22 |
| socle, cosocle | C22×C32 | C24 |
| prime radical | C2×#3830 | C2 |
| hypercenter | C2×D4 | D32 |
| hypocenter | C32 | #520 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×D4×Dic3 | C2 | semidirect |
| 3. C2×#3724 | C2 | semidirect |
| 4. #63957 | C2 | semidirect |
| 5. #63952 | C2 | semidirect |
| 6. #63900 | C2 | semidirect |
| 7. #63874 | C2 | semidirect |
| 8. #63844 | C2 | semidirect |
| 13. #3830 | C4 | semidirect |
| 30. D4×Dic3 | D3 | semidirect |
| 41. C32×D4 | C2×C4 | semidirect |
| 43. #638 | C2×C4 | semidirect |
| 44. C2×C3⋊Dic3 | C2×C4 | semidirect |
| 47. C4×C3⋊D3 | C2×C4 | semidirect |
| 48. #634 | C2×C4 | semidirect |
| 111. C3×D4 | C4×D3 | semidirect |
| 183. C32 | #520 | semidirect |
| 188. D4 | #624 | semidirect |
| 223. C3 | #5546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3830 | 2 |
| C3×D4×Dic3 | 2 |
| C2×#3724 | 2 |
| #63957 | 2 |
| #63952 | 2 |
| #63900 | 2 |
| #63874 | 2 |
| #63844 | 2 |
| #5546 | 3 |