Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
304 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×C3⋊D3 |
| commutator, socle, cosocle | C2×C33 | C23 |
| Fitting | C33×C4 | C22 |
| hypercenter | C4 | D3×C3⋊D3 |
| hypocenter | C33 | #41 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 2. C3×C4×C3⋊D3 | C2 | semidirect |
| 3. C32×Dic6 | C2 | semidirect |
| 4. #6292 | C2 | semidirect |
| 5. #6289 | C2 | semidirect |
| 19. C4×C3⋊D3 | D3 | semidirect |
| 21. C3×Dic6 | D3 | semidirect |
| 41. C33 | #41 | semidirect |
| 52. Dic6 | C3⋊D3 | semidirect |
| 75. C32 | #235 | semidirect |
| 76. C32 | #239 | semidirect |
| 96. C3 | #3799 | semidirect |
| 97. C3 | #3832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊(C3⋊(C3⋊D3)) | 2 |
| C3×C4×C3⋊D3 | 2 |
| C32×Dic6 | 2 |
| #6292 | 2 |
| #6289 | 2 |
| #3832 | 3 |
| #3799 | 3 |