Finite Group DatabasebetaFinite Group DatabasebetaOrder 14528.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20300283 | C2 | semidirect |
| 2. #20300279 | C2 | semidirect |
| 3. #20300278 | C2 | semidirect |
| 5. #20300268 | C2 | semidirect |
| 6. #20300267 | C2 | semidirect |
| 7. #20300253 | C2 | semidirect |
| 9. #20300247 | C2 | semidirect |
| 10. #20300246 | C2 | semidirect |
| 11. C2×C4⋊C4×C227 | C2 | semidirect |
| 72. C227 | #552 | semidirect |
| 84. C2×C4⋊C4 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20300283 | 2 |
| #20300279 | 2 |
| #20300278 | 2 |
| #20300271 | 2 |
| #20300268 | 2 |
| #20300267 | 2 |
| #20300253 | 2 |
| C4×C22⋊D227 | 2 |
| #20300247 | 2 |
| #20300246 | 2 |
| C2×C4⋊C4×C227 | 2 |
| #552 | 227 |