Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
279 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 46 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 | C9⋊((C22⋊C9)⋊C2) |
| commutator, cosocle, hypocenter | C22⋊#6855 | C2 |
| Frattini | C33 | C3⋊S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C22⋊#6855 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22⋊#6855 | C2 | semidirect |
| 23. C22×C3×C9 | D9 | semidirect |
| 28. C3×C22⋊C9 | D9 | semidirect |
| 69. C3×C9 | (C22⋊C9)⋊C2 | semidirect |
| 113. C22 | #92197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊#6855 | 2 |
| C3×C3⋊((C22⋊C9)⋊C2) | 3 |
| C3×#6233 | 3 |
| #92197 | 4 |