Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
180 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 180 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 | #10619770 |
| commutator, Fitting, cosocle, hypocenter | C22×C32⋊C9 | C2×C3 |
| Frattini | C33 | D3×A4 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| prime radical | C22×#4181 | C3 |
| LCS | G ▷ C22×C32⋊C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757406 | C2 | semidirect |
| 30. C3×C22⋊C9 | D9 | semidirect |
| 134. C22 | #92176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757406 | 2 |
| C3⋊D3×C22⋊C9 | 3 |
| C22×#4181 | 3 |
| #92176 | 4 |