Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
225 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 225 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D9 |
| commutator, cosocle | C23×C9 | C23 |
| Frattini, socle, prime radical | C23×C3 | C22×D3 |
| Fitting | C2×C9×C4⋊C4 | C2 |
| hypercenter | C2×C4⋊C4 | D9 |
| hypocenter | C9 | #398 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 95. C9 | #398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×C4⋊C4 | 2 |
| C2×C4⋊Dic9 | 2 |
| C2×Dic9⋊C4 | 2 |
| C9⋊#95 | 2 |
| #4981 | 3 |