Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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. C22×#6903 | C2 | semidirect |
| 2. C2×#92319 | C2 | semidirect |
| 3. #11757623 | C2 | semidirect |
| 13. C22×C3×C27 | D3 | semidirect |
| 16. #6903 | D4 | semidirect |
| 41. C3×C27 | #67 | semidirect |
| 96. C22 | #92319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6903 | 2 |
| C2×#92319 | 2 |
| #11757623 | 2 |
| #10619984 | 3 |
| #67×C27 | 3 |