Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
600 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 193 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 | C23×C3⋊D3 |
| commutator, socle, prime radical, cosocle | C22×C32 | C24 |
| Fitting | C32×#125 | C2 |
| hypercenter | #125 | C3⋊D3 |
| hypocenter | C32 | #557 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 60. #634 | Q8 | semidirect |
| 160. C32 | #557 | semidirect |
| 190. C3 | #5685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#125 | 2 |
| #64099 | 2 |
| #64098 | 2 |
| #64097 | 2 |
| #64096 | 2 |
| C4×#634 | 2 |
| #5685 | 3 |