Finite Group DatabasebetaFinite Group Databasebeta← (C3⋊Dic3)⋊(C22⋊C9) #13047064
Order 1296.
206 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | (C3⋊D3)⋊A4 |
| commutator, hypocenter | C22×C32 | C4×C9 |
| Frattini | C2×C32 | D3×A4 |
| Fitting, prime radical, cosocle | C23×C33 | C2×C3 |
| socle | C23×C32 | C3×D3 |
| LCS | G ▷ C22×C32 | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C32⋊(C22⋊C9) | C4 | semidirect |
| 12. C22×C3⋊Dic3 | C9 | semidirect |
| 22. C3×C22⋊C9 | Dic3 | semidirect |
| 59. C22×C32 | C4×C9 | semidirect |
| 62. C3⋊Dic3 | C22⋊C9 | semidirect |
| 126. C32 | C4×C22⋊C9 | semidirect |
| 150. C22 | (C3⋊Dic3)⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32⋊(C22⋊C9) | 2 |
| C22×C3×C3⋊Dic3 | 3 |
| Dic3×C22⋊C9 | 3 |
| (C3⋊Dic3)⋊C9 | 4 |