Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 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. #28357307 | C2 | direct (N × H) |
| 2. C2×#20294107 | C2 | semidirect |
| 3. C2×#20294106 | C2 | semidirect |
| 4. C2×#20294105 | C2 | semidirect |
| 5. C22×#16812365 | C2 | semidirect |
| 7. #20294107 | C22 | semidirect |
| 8. #20294106 | C22 | semidirect |
| 9. #20294105 | C22 | semidirect |
| 13. C2×#16812365 | C22 | semidirect |
| 46. C2×C433 | #131 | semidirect |
| 49. C433 | C2×#131 | semidirect |
| 97. C2 | #28357307 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28357307 | 2 |
| C2×#20294107 | 2 |
| C2×#20294106 | 2 |
| C2×#20294105 | 2 |
| C22×#16812365 | 2 |
| C2×#20294096 | 2 |
| C2×#131 | 433 |