Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
357 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 123 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 | C4×D4×C9 | C2 |
| hypercenter | C4×D4 | D9 |
| hypocenter | C9 | #553 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×D4×C9 | C2 | semidirect |
| 2. #63501 | C2 | semidirect |
| 3. #63492 | C2 | semidirect |
| 4. #63492 | C2 | semidirect |
| 5. #63488 | C2 | semidirect |
| 6. C2×C4⋊Dic9 | C2 | semidirect |
| 7. #63460 | C2 | semidirect |
| 8. #63445 | C2 | semidirect |
| 9. #611⋊C4 | C2 | semidirect |
| 10. C4×D36 | C2 | semidirect |
| 11. #63432 | C2 | semidirect |
| 116. C4×D4 | D9 | semidirect |
| 185. C9 | #553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C9 | 2 |
| #63501 | 2 |
| #63492 | 2 |
| #63488 | 2 |
| C2×C4⋊Dic9 | 2 |
| #63460 | 2 |
| #63445 | 2 |
| #611⋊C4 | 2 |
| C4×D36 | 2 |
| #63432 | 2 |
| #5565 | 3 |