Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
230 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 230 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, hypercenter | C9 | (C3⋊D3)⋊A4 |
| commutator, cosocle, hypocenter | C22×H(3,𝔽3) | C2×C32 |
| Frattini | C32 | C3×D3×A4 |
| Fitting | C22×#737 | C2×C3 |
| socle | C22×C3 | C3×(C3⋊D3)⋊C3 |
| LCS | G ▷ C22×H(3,𝔽3) | |
| UCS | C1 ◁ C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757862 | C2 | semidirect |
| 2. C22×#4208 | C3 | semidirect |
| 4. #10619773 | C3 | semidirect |
| 5. #10619772 | C3 | semidirect |
| 6. #10619771 | C3 | semidirect |
| 8. C22×#737 | C2×C3 | semidirect |
| 12. C3×C9×A4 | D3 | semidirect |
| 17. #66362 | C2×C3 | semidirect |
| 18. #66361 | C2×C3 | semidirect |
| 29. #4208 | A4 | semidirect |
| 56. #737 | C2×A4 | semidirect |
| 174. C22 | #92280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757862 | 2 |
| C22×#4208 | 3 |
| D3×C9×A4 | 3 |
| #10619773 | 3 |
| #10619772 | 3 |
| #10619771 | 3 |
| #92280 | 4 |