Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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. #28357308 | C2 | semidirect |
| 2. #28357307 | C2 | semidirect |
| 3. #28357291 | C2 | semidirect |
| 4. #28357285 | C2 | semidirect |
| 5. #28357284 | C2 | semidirect |
| 6. #28357274 | C2 | semidirect |
| 18. #20294087 | C4 | semidirect |
| 19. #20294086 | C4 | semidirect |
| 20. #20294082 | C4 | semidirect |
| 22. SD16×C433 | C4 | semidirect |
| 51. C433 | #444 | semidirect |
| 64. SD16 | #13181884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28357308 | 2 |
| #28357307 | 2 |
| #28357291 | 2 |
| #28357285 | 2 |
| #28357284 | 2 |
| #28357274 | 2 |
| #28357241 | 2 |
| #444 | 433 |