Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
186 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 16 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 | #10619743 |
| commutator, cosocle, hypocenter | C32⋊(C22⋊C9) | C2×C3 |
| Frattini | C33 | C3×S4 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C32⋊(C22⋊C9) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757452 | C2 | semidirect |
| 3. #10619761 | C3 | semidirect |
| 9. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 127. C22 | #92163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757452 | 2 |
| C3×#638⋊C3 | 3 |
| #10619761 | 3 |
| #92163 | 4 |