Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20299169 | C2 | semidirect |
| 3. #20298940 | C2 | semidirect |
| 4. #20298923 | C2 | semidirect |
| 5. #20298844 | C2 | semidirect |
| 6. #20298827 | C2 | semidirect |
| 7. #20298751 | C2 | semidirect |
| 8. #20298739 | C2 | semidirect |
| 9. #408×C113 | C2 | semidirect |
| 10. C22×Dic226 | C22 | semidirect |
| 21. #16813601 | C22 | semidirect |
| 27. #16813581 | C22 | semidirect |
| 28. #16813556 | C22 | semidirect |
| 29. #16813554 | C22 | semidirect |
| 30. #16813547 | C22 | semidirect |
| 31. #16813547 | C22 | semidirect |
| 35. C2×M16×C113 | C22 | semidirect |
| 36. C22×C8×C113 | C22 | semidirect |
| 38. C22⋊C8×C113 | C22 | semidirect |
| 138. C113 | #3200 | semidirect |
| 147. #408 | D113 | semidirect |
| 153. C2×M16 | C2×D113 | semidirect |
| 154. C22×C8 | C2×D113 | semidirect |
| 176. C22⋊C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299169 | 2 |
| #20299162 | 2 |
| #20298940 | 2 |
| #20298923 | 2 |
| #20298844 | 2 |
| #20298827 | 2 |
| #20298751 | 2 |
| #20298739 | 2 |
| #408×C113 | 2 |
| #3200 | 113 |