Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20299226 | C2 | semidirect |
| 3. #20298961 | C2 | semidirect |
| 4. #20298959 | C2 | semidirect |
| 5. #20298954 | C2 | semidirect |
| 6. #20298943 | C2 | semidirect |
| 7. #20298602 | C2 | semidirect |
| 8. #20298599 | C2 | semidirect |
| 9. C2×#16813544 | C2 | semidirect |
| 10. #20298553 | C2 | semidirect |
| 11. #416×C113 | C2 | semidirect |
| 15. #16813621 | C22 | semidirect |
| 18. #16813613 | C22 | semidirect |
| 26. #16813546 | C22 | semidirect |
| 29. #16813543 | C22 | semidirect |
| 32. #16813532 | C22 | semidirect |
| 33. C8×Dic113 | C22 | semidirect |
| 37. #103×C113 | C22 | semidirect |
| 38. #103×C113 | C22 | semidirect |
| 39. #102×C113 | C22 | semidirect |
| 40. #102×C113 | C22 | semidirect |
| 136. C113 | #3136 | semidirect |
| 145. #416 | D113 | semidirect |
| 166. #103 | C2×D113 | semidirect |
| 167. #103 | C2×D113 | semidirect |
| 173. #102 | C2×D113 | semidirect |
| 174. #102 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299226 | 2 |
| #20299162 | 2 |
| #20298961 | 2 |
| #20298959 | 2 |
| #20298954 | 2 |
| #20298943 | 2 |
| #20298602 | 2 |
| #20298599 | 2 |
| C2×#16813544 | 2 |
| #20298553 | 2 |
| #416×C113 | 2 |
| #3136 | 113 |