Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×C3⋊D3 |
| commutator | C2×C33 | C2×C4 |
| Fitting, socle, cosocle | C22×C33 | C22 |
| prime radical | C22×C32×D3 | C2 |
| hypocenter | C33 | C22⋊C4 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C2×C3×C3⋊Dic3 | C2 | semidirect |
| 9. C2×C32×D3 | C4 | semidirect |
| 17. C2×C3⋊Dic3 | D3 | semidirect |
| 33. C2×C3×D3 | Dic3 | semidirect |
| 39. C33 | C22⋊C4 | semidirect |
| 67. C2×D3 | C3⋊Dic3 | semidirect |
| 74. C32 | (C2×D3)⋊C4 | semidirect |
| 75. C32 | #217 | semidirect |
| 97. C3 | (C2×D3)⋊Dic3 | semidirect |
| 98. C3 | #3757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D3 | 2 |
| C2×C3⋊(C3⋊Dic3) | 2 |
| C2×C3×C3⋊Dic3 | 2 |
| #3757 | 3 |
| (C2×D3)⋊Dic3 | 3 |