Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
136 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 41 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 | C22×C3×C9 | C22 |
| socle | C2×C32 | C22×D3 |
| hypercenter | C22 | D3×D9 |
| hypocenter | C3×C9 | #41 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #6233 | C2 | semidirect |
| 2. C3×#611 | C2 | semidirect |
| 3. C2×C9×Dic3 | C2 | semidirect |
| 4. #6192 | C2 | semidirect |
| 5. (C3⋊D9)⋊C4 | C2 | semidirect |
| 6. Dic3×D9 | C2 | semidirect |
| 7. #6189 | C2 | semidirect |
| 27. #611 | D3 | semidirect |
| 55. C3×C9 | #41 | semidirect |
| 64. C2×Dic3 | D9 | semidirect |
| 102. C9 | #237 | semidirect |
| 129. C3 | #3697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6233 | 2 |
| C3×#611 | 2 |
| C2×C9×Dic3 | 2 |
| #6192 | 2 |
| (C3⋊D9)⋊C4 | 2 |
| Dic3×D9 | 2 |
| #6189 | 2 |
| #3804 | 3 |
| #3697 | 3 |