Finite Group DatabasebetaFinite Group DatabasebetaOrder 14528.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20300286 | C2 | semidirect |
| 2. #20300283 | C2 | semidirect |
| 3. #20300281 | C2 | semidirect |
| 4. #20300277 | C2 | semidirect |
| 5. #20300274 | C2 | semidirect |
| 6. #20300274 | C2 | semidirect |
| 7. #20300273 | C2 | semidirect |
| 8. #20300271 | C2 | semidirect |
| 9. #20300266 | C2 | semidirect |
| 10. #20300266 | C2 | semidirect |
| 12. #20300253 | C2 | semidirect |
| 13. C4×C22⋊D227 | C2 | semidirect |
| 14. #20300246 | C2 | semidirect |
| 15. C22⋊Q8×C227 | C2 | semidirect |
| 103. C227 | #542 | semidirect |
| 115. C22⋊Q8 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20300286 | 2 |
| #20300283 | 2 |
| #20300281 | 2 |
| #20300277 | 2 |
| #20300274 | 2 |
| #20300273 | 2 |
| #20300271 | 2 |
| #20300266 | 2 |
| #20300261 | 2 |
| #20300253 | 2 |
| C4×C22⋊D227 | 2 |
| #20300246 | 2 |
| C22⋊Q8×C227 | 2 |
| #542 | 227 |