Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
1191 conjugacy classes of subgroups; only the 513 normal subgroups are shown.
This group has 1191 conjugacy classes of subgroups — too many to draw. Only its 513 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C24×D9 |
| commutator, cosocle | C2×C9 | C25 |
| Frattini, socle | C2×C3 | C24×D3 |
| Fitting | C9×2−1+4 | C2 |
| hypercenter | 2−1+4 | D9 |
| hypocenter | C9 | C2×2−1+4 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×2−1+4 | C2 | semidirect |
| 2. #63716 | C2 | semidirect |
| 3. #41×D9 | C2 | semidirect |
| 4. #63713 | C2 | semidirect |
| 5. C2×Q8×D9 | C2 | semidirect |
| 7. C9×#41 | C22 | semidirect |
| 8. C2×Q8×C9 | C22 | semidirect |
| 9. #3701 | C22 | semidirect |
| 11. Q8×D9 | C22 | semidirect |
| 12. #3699 | C22 | semidirect |
| 14. #3697 | C22 | semidirect |
| 16. C2×Dic18 | C22 | semidirect |
| 51. 2−1+4 | D9 | direct (N × H) |
| 67. D9 | 2−1+4 | direct (N × H) |
| 71. #41 | C2×D9 | semidirect |
| 75. C2×Q8 | C2×D9 | semidirect |
| 84. C9 | C2×2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×2−1+4 | 2 |
| #63716 | 2 |
| #41×D9 | 2 |
| #63713 | 2 |
| C2×Q8×D9 | 2 |
| D3×2−1+4 | 3 |