Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #28357213 | C2 | semidirect |
| 2. #28357211 | C2 | semidirect |
| 3. #28357207 | C2 | semidirect |
| 4. #28357202 | C2 | semidirect |
| 5. #28357200 | C2 | semidirect |
| 7. C4×Dic866 | C2 | semidirect |
| 8. C4×C22⋊D433 | C2 | semidirect |
| 9. #28357179 | C2 | semidirect |
| 10. C42×D433 | C2 | semidirect |
| 11. C4×D4×C433 | C2 | semidirect |
| 74. C433 | #529 | semidirect |
| 84. C4×D4 | D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28357213 | 2 |
| #28357211 | 2 |
| #28357207 | 2 |
| #28357202 | 2 |
| #28357200 | 2 |
| #28357191 | 2 |
| C4×Dic866 | 2 |
| C4×C22⋊D433 | 2 |
| #28357179 | 2 |
| C42×D433 | 2 |
| C4×D4×C433 | 2 |
| #529 | 433 |