Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 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×#20294082 | C2 | semidirect |
| 2. #28357194 | C2 | semidirect |
| 3. #28357141 | C2 | semidirect |
| 4. C22⋊#16812358 | C2 | semidirect |
| 5. C22×D4×C433 | C2 | semidirect |
| 6. C2×D1732 | C22 | semidirect |
| 9. C2×#16812358 | C22 | semidirect |
| 10. C4⋊Dic433 | C22 | semidirect |
| 29. D4×C433 | D4 | semidirect |
| 39. C22×C433 | D8 | semidirect |
| 53. C433 | #447 | semidirect |
| 55. C22×D4 | D433 | semidirect |
| 81. D4 | C22⋊D433 | semidirect |
| 96. C22 | #20294082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294082 | 2 |
| #28357194 | 2 |
| #28357141 | 2 |
| C22⋊#16812358 | 2 |
| C22×D4×C433 | 2 |
| #447 | 433 |