Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
372 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D9 |
| commutator, cosocle | C4×C9 | C24 |
| Frattini | C3×C4 | C23×D3 |
| Fitting | C9×#137 | C2 |
| socle | C2×C3 | C2×D3×D4 |
| hypercenter | #137 | D9 |
| hypocenter | C9 | #578 |
| LCS | G ▷ C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63716 | C2 | semidirect |
| 2. #63713 | C2 | semidirect |
| 3. C9×#137 | C2 | semidirect |
| 4. #63513 | C2 | semidirect |
| 5. C2×#3674 | C2 | semidirect |
| 6. #63480 | C2 | semidirect |
| 7. Q16×D9 | C2 | semidirect |
| 8. #63478 | C2 | semidirect |
| 9. #63477 | C2 | semidirect |
| 10. #63471 | C2 | semidirect |
| 11. #63469 | C2 | semidirect |
| 129. #137 | D9 | semidirect |
| 210. C9 | #578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63716 | 2 |
| #63713 | 2 |
| C9×#137 | 2 |
| #63513 | 2 |
| C2×#3674 | 2 |
| #63480 | 2 |
| Q16×D9 | 2 |
| #63478 | 2 |
| #63477 | 2 |
| #63471 | 2 |
| #63469 | 2 |
| #5779 | 3 |