Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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×#1113 |
| commutator, socle, cosocle | C2×C33 | C23 |
| Fitting | C33×C4 | C22 |
| hypercenter | C4 | #1113 |
| 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. C3×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C3×C4×C3⋊D3 | C2 | semidirect |
| 3. C3×#634 | C2 | semidirect |
| 4. #6295 | C2 | semidirect |
| 5. #6294 | C2 | semidirect |
| 14. C4⋊(C3⋊D3) | D3 | semidirect |
| 15. C4×C3⋊D3 | D3 | semidirect |
| 16. #634 | D3 | semidirect |
| 61. C33 | #41 | semidirect |
| 123. C32 | #235 | semidirect |
| 124. C32 | #237 | semidirect |
| 125. C32 | #239 | semidirect |
| 155. C3 | #3795 | semidirect |
| 156. C3 | #3796 | semidirect |
| 157. C3 | #3799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4⋊(C3⋊D3) | 2 |
| C3×C4×C3⋊D3 | 2 |
| C3×#634 | 2 |
| #6295 | 2 |
| #6294 | 2 |
| #3799 | 3 |
| #3796 | 3 |
| #3795 | 3 |