Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
300 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D9 |
| commutator, cosocle | C22×C9 | C24 |
| Frattini, socle, prime radical | C22×C3 | C23×D3 |
| Fitting | C4×Q8×C9 | C2 |
| hypercenter | C4×Q8 | D9 |
| hypocenter | C9 | #557 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 28. Q8×C9 | Q8 | semidirect |
| 97. C9 | #557 | semidirect |
| 99. Q8 | Dic18 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C9 | 2 |
| Q8×Dic9 | 2 |
| #63452 | 2 |
| #63450 | 2 |
| #63432 | 2 |
| C4×Dic18 | 2 |
| #5569 | 3 |