Finite Group DatabasebetaFinite Group DatabasebetaOrder 14528.
242 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20300268 | C2 | semidirect |
| 2. #20300267 | C2 | semidirect |
| 3. #20300266 | C2 | semidirect |
| 4. #20300266 | C2 | semidirect |
| 5. #20300265 | C2 | semidirect |
| 6. #20300264 | C2 | semidirect |
| 9. C22⋊Q8×C227 | C2 | semidirect |
| 11. C2×Dic454 | C22 | semidirect |
| 12. C2×Dic454 | C22 | semidirect |
| 16. C4⋊Dic227 | C22 | semidirect |
| 17. C4⋊Dic227 | C22 | semidirect |
| 18. Dic227⋊C4 | C22 | semidirect |
| 19. Dic227⋊C4 | C22 | semidirect |
| 20. Dic227⋊C4 | C22 | semidirect |
| 26. C2×Q8×C227 | C22 | semidirect |
| 28. C4⋊C4×C227 | C22 | semidirect |
| 29. C4⋊C4×C227 | C22 | semidirect |
| 33. C22×D227 | Q8 | semidirect |
| 70. C227 | #543 | semidirect |
| 78. C22⋊Q8 | D227 | semidirect |
| 84. C2×Q8 | C2×D227 | semidirect |
| 94. C4⋊C4 | C2×D227 | semidirect |
| 95. C4⋊C4 | C2×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20300268 | 2 |
| #20300267 | 2 |
| #20300266 | 2 |
| #20300265 | 2 |
| #20300264 | 2 |
| C2×(C2×D227)⋊C4 | 2 |
| C22⋊C4×D227 | 2 |
| C22⋊Q8×C227 | 2 |
| #543 | 227 |