Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
422 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#157 |
| commutator, socle | C2×C32 | C23×C4 |
| Fitting | C32×#41 | C4 |
| prime radical | #41×C3⋊D3 | C2 |
| cosocle | C3⋊Dic3 | C24 |
| hypercenter | #41 | #157 |
| hypocenter | C32 | #568 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #64289 | C2 | semidirect |
| 3. #64287 | C2 | semidirect |
| 4. #64283 | C2 | semidirect |
| 5. C2×#3788 | C2 | semidirect |
| 13. #3792 | C22 | semidirect |
| 14. C2×#622 | C22 | semidirect |
| 17. #3788 | C22 | semidirect |
| 18. #3787 | C22 | semidirect |
| 92. C32 | #568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C3⋊D3 | 2 |
| #64289 | 2 |
| #64287 | 2 |
| #64283 | 2 |
| C2×#3788 | 2 |
| #568 | 9 |