Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
311 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C9×A4 | C2×C3 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C3×C9×A4 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×C22⋊H(3,𝔽3) | C2 | semidirect |
| 2. C3⋊(C9⋊S4) | C3 | semidirect |
| 7. C22×C32×C9 | D3 | semidirect |
| 11. C3×C9×A4 | C2×C3 | semidirect |
| 13. C32⋊(C22⋊C9) | D3 | semidirect |
| 40. C22⋊H(3,𝔽3) | D9 | semidirect |
| 50. C32×C9 | S4 | semidirect |
| 78. C22×C32 | C3⋊D9 | semidirect |
| 89. C3×A4 | C3×D9 | semidirect |
| 95. C22×C9 | (C3⋊D3)⋊C3 | semidirect |
| 159. C32 | C9⋊S4 | semidirect |
| 164. C9 | (C3⋊S4)⋊C3 | semidirect |
| 179. C22 | #92297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C22⋊H(3,𝔽3) | 2 |
| C3⋊(C9⋊S4) | 3 |
| C3⋊((C3⋊S4)⋊C3) | 3 |
| C3×#6233 | 3 |
| #10619746 | 3 |
| #92297 | 4 |