Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
197 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 29 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 | A4×(C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | C22×H(3,𝔽3) | C2×C32 |
| Frattini | C32 | C3×D3×A4 |
| Fitting | C22×#732 | C2×C3 |
| socle | C22×C3 | C3×(C3⋊D3)⋊C3 |
| LCS | G ▷ C22×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757806 | C2 | semidirect |
| 2. #10620072 | C3 | semidirect |
| 4. C22×#4178 | C3 | semidirect |
| 5. #10619773 | C3 | semidirect |
| 6. #10619772 | C3 | semidirect |
| 9. #66437 | C2×C3 | semidirect |
| 10. C3×C9×A4 | D3 | semidirect |
| 11. C22×#732 | C2×C3 | semidirect |
| 17. #66361 | C2×C3 | semidirect |
| 31. #4178 | A4 | semidirect |
| 57. #732 | C2×A4 | semidirect |
| 169. C22 | #92280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757806 | 2 |
| #10620072 | 3 |
| D3×C9×A4 | 3 |
| C22×#4178 | 3 |
| #10619773 | 3 |
| #10619772 | 3 |
| #92280 | 4 |