Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
178 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 45 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×D3×D9 |
| commutator, cosocle | C2×C3×C9 | C23 |
| Frattini | C2×C3 | C2×D32 |
| Fitting | C3×C4×C9 | C22 |
| socle | C2×C32 | C22×D3 |
| hypercenter | C4 | D3×D9 |
| hypocenter | C3×C9 | C2×D4 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D3×D9 | C2 | semidirect |
| 2. C4⋊(C3⋊D9) | C2 | semidirect |
| 3. C9×D12 | C2 | semidirect |
| 4. C3×C4×D9 | C2 | semidirect |
| 5. #6195 | C2 | semidirect |
| 8. C2×C3⋊D9 | C22 | semidirect |
| 9. C2×D3×C9 | C22 | semidirect |
| 12. C3×C4×C9 | C22 | semidirect |
| 13. C3×Dic9 | C22 | semidirect |
| 24. C4×D9 | D3 | semidirect |
| 28. C3×D9 | D4 | semidirect |
| 43. C4×C9 | C2×D3 | semidirect |
| 44. Dic9 | C2×D3 | semidirect |
| 45. C3×C9 | C2×D4 | semidirect |
| 55. D12 | D9 | direct (N × H) |
| 66. D9 | D12 | direct (N × H) |
| 76. C2×D3 | C2×D9 | semidirect |
| 79. C3×C4 | C2×D9 | semidirect |
| 84. C9 | C2×D12 | semidirect |
| 105. C4 | D3×D9 | semidirect |
| 107. C3 | D4×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D9 | 2 |
| C4⋊(C3⋊D9) | 2 |
| C9×D12 | 2 |
| C3×C4×D9 | 2 |
| #6195 | 2 |
| D3×D12 | 3 |
| D4×D9 | 3 |