Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
157 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 157 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #66440⋊C2 |
| commutator, cosocle, hypocenter | (C3×A4)⋊C9 | C2×C3 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C9⋊C9 | D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| prime radical | #10619754 | C3 |
| LCS | G ▷ (C3×A4)⋊C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757787 | C2 | semidirect |
| 9. C22×C9⋊C9 | D3 | semidirect |
| 16. (C22⋊C9)⋊C9 | D3 | semidirect |
| 17. C9×C22⋊C9 | D3 | semidirect |
| 50. C9⋊C9 | S4 | semidirect |
| 140. C22 | #92308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757787 | 2 |
| #10619754 | 3 |
| (C3⋊S4)⋊C9 | 3 |
| C9×(C22⋊C9)⋊C2 | 3 |
| ((C22⋊C9)⋊C2)⋊C9 | 3 |
| #611⋊C9 | 3 |
| #92308 | 4 |