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 | C3×C4×C9 | C22 |
| socle | C2×C32 | C22×D3 |
| hypercenter | C4 | D3×D9 |
| hypocenter | C3×C9 | #41 |
| 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. C4×C3⋊D9 | C2 | semidirect |
| 2. C3×D36 | C2 | semidirect |
| 3. C9×Dic6 | C2 | semidirect |
| 4. #6192 | C2 | semidirect |
| 5. Dic3×D9 | C2 | semidirect |
| 20. D36 | D3 | semidirect |
| 42. C3×C9 | #41 | semidirect |
| 53. Dic6 | D9 | semidirect |
| 78. C9 | #237 | semidirect |
| 98. C3 | #3701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊D9 | 2 |
| C3×D36 | 2 |
| C9×Dic6 | 2 |
| #6192 | 2 |
| Dic3×D9 | 2 |
| #3796 | 3 |
| #3701 | 3 |