Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 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 | C9×#127 | C2 |
| hypercenter | #127 | D9 |
| hypocenter | C9 | #560 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#127 | C2 | semidirect |
| 2. #63501 | C2 | semidirect |
| 3. #63499 | C2 | semidirect |
| 4. #63497 | C2 | semidirect |
| 5. #63438 | C2 | semidirect |
| 9. C2×D4×C9 | C22 | semidirect |
| 11. C22×Dic9 | C22 | semidirect |
| 12. C42×C9 | C22 | semidirect |
| 14. #3676 | C22 | semidirect |
| 16. Dic9⋊C4 | C22 | semidirect |
| 51. #127 | D9 | semidirect |
| 73. C2×D4 | C2×D9 | semidirect |
| 79. C42 | C2×D9 | semidirect |
| 88. C9 | #560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#127 | 2 |
| #63501 | 2 |
| #63499 | 2 |
| #63497 | 2 |
| #63438 | 2 |
| #5720 | 3 |