Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
197 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3 | C3×(C3⋊S4)⋊C3 |
| commutator, cosocle, hypocenter | C22⋊H(3,𝔽3) | C2×C32 |
| Frattini | C32 | C32×S4 |
| Fitting | C22×C3×3−1+2 | D3 |
| socle | C22×C3 | C3×(C3⋊D3)⋊C3 |
| hypercenter | C9 | (C3⋊S4)⋊C3 |
| LCS | G ▷ C22⋊H(3,𝔽3) | |
| UCS | C1 ◁ C3 ◁ C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757853 | C2 | semidirect |
| 2. #10620044 | C3 | semidirect |
| 4. #10619747 | C3 | semidirect |
| 5. #10619741 | C3 | semidirect |
| 6. #10619740 | C3 | semidirect |
| 8. C22×C3×3−1+2 | D3 | semidirect |
| 11. #66436 | C2×C3 | semidirect |
| 16. #66358 | C2×C3 | semidirect |
| 18. #66357 | C2×C3 | semidirect |
| 61. C3×3−1+2 | S4 | semidirect |
| 187. C22 | #6913⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757853 | 2 |
| #10620044 | 3 |
| #67×3−1+2 | 3 |
| #10619747 | 3 |
| #10619741 | 3 |
| #10619740 | 3 |
| #6913⋊C2 | 4 |