Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C22×D9 |
| commutator, cosocle | C2×C9 | C23×C3 |
| Frattini | C2×C3 | C22×C3×D3 |
| Fitting | C3×D4×C9 | C2 |
| socle | C2×C32 | C22×D3 |
| hypercenter | C3×D4 | D9 |
| hypocenter | C9 | C3×#41 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2×C3 ◁ C3×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×D4×C9 | C2 | semidirect |
| 2. C3×#611 | C2 | semidirect |
| 3. C2×C3×Dic9 | C2 | semidirect |
| 4. C3×C4×D9 | C2 | semidirect |
| 5. C3×Dic18 | C2 | semidirect |
| 7. #3699 | C3 | direct (N × H) |
| 19. D4×C9 | C2×C3 | semidirect |
| 20. #611 | C2×C3 | semidirect |
| 21. C2×Dic9 | C2×C3 | semidirect |
| 22. C4×D9 | C2×C3 | semidirect |
| 23. Dic18 | C2×C3 | semidirect |
| 41. C3×C9 | #41 | semidirect |
| 45. C3×D4 | D9 | semidirect |
| 76. C9 | C3×#41 | semidirect |
| 79. D4 | C3×D9 | semidirect |
| 96. C3 | #3699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×C9 | 2 |
| C3×#611 | 2 |
| C2×C3×Dic9 | 2 |
| C3×C4×D9 | 2 |
| C3×Dic18 | 2 |
| C3×#237 | 3 |
| #3699 | 3 |