Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
202 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×#20294105 | C2 | semidirect |
| 2. #28357277 | C2 | semidirect |
| 3. C22⋊#16812365 | C2 | semidirect |
| 6. C2×#16812365 | C22 | semidirect |
| 18. C22×D433 | C8 | semidirect |
| 34. C22×C433 | C2×C8 | semidirect |
| 41. C2×D433 | C2×C8 | semidirect |
| 52. D433 | C22⋊C8 | semidirect |
| 53. C433 | C2×C22⋊C8 | semidirect |
| 95. C22 | #20294105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294105 | 2 |
| #28357277 | 2 |
| C22⋊#16812365 | 2 |
| C22×C4×D433 | 2 |
| C2×C22⋊C8 | 433 |