Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
316 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 316 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757841 | C2 | semidirect |
| 2. C22×C3×#272 | C3 | semidirect |
| 4. #10619773 | C3 | semidirect |
| 6. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 9. C3×C22⋊H(3,𝔽3) | D3 | semidirect |
| 12. #66363 | C2×C3 | semidirect |
| 21. C3×#272 | A4 | semidirect |
| 30. C32×A4 | C3×D3 | semidirect |
| 44. C3×H(3,𝔽3) | C2×A4 | semidirect |
| 166. C22 | #92281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757841 | 2 |
| C22×C3×#272 | 3 |
| D3×C22⋊H(3,𝔽3) | 3 |
| #10619773 | 3 |
| #92281 | 4 |