Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
441 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 441 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C22×C3 | C23×D3 |
| Fitting | C2×C9×C4⋊C4 | C2 |
| hypercenter | C2×C4⋊C4 | D9 |
| hypocenter | C9 | #537 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3697 | C2 | semidirect |
| 2. C2×C9×C4⋊C4 | C2 | semidirect |
| 3. #63492 | C2 | semidirect |
| 4. #63459 | C2 | semidirect |
| 5. #63457 | C2 | semidirect |
| 26. C2×C4×C9 | D4 | semidirect |
| 61. C2×C4⋊C4 | D9 | semidirect |
| 100. C9 | #537 | semidirect |
| 110. C2×C4 | D36 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3697 | 2 |
| C2×C9×C4⋊C4 | 2 |
| #63492 | 2 |
| #63459 | 2 |
| #63457 | 2 |
| #5510 | 3 |