Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #20299078 | C2 | semidirect |
| 3. #20298925 | C2 | semidirect |
| 4. #20298924 | C2 | semidirect |
| 5. #20298918 | C2 | semidirect |
| 6. #20298913 | C2 | semidirect |
| 7. #20298641 | C2 | semidirect |
| 8. #20298602 | C2 | semidirect |
| 9. C2×#16813544 | C2 | semidirect |
| 10. #20298564 | C2 | semidirect |
| 11. #427×C113 | C2 | semidirect |
| 23. #16813580 | C22 | semidirect |
| 25. C4⋊C4×D113 | C22 | semidirect |
| 26. #16813555 | C22 | semidirect |
| 27. #16813553 | C22 | semidirect |
| 32. #16813534 | C22 | semidirect |
| 33. #16813534 | C22 | semidirect |
| 37. #107×C113 | C22 | semidirect |
| 38. #107×C113 | C22 | semidirect |
| 39. #106×C113 | C22 | semidirect |
| 40. #106×C113 | C22 | semidirect |
| 135. C113 | #3096 | semidirect |
| 143. #427 | D113 | semidirect |
| 165. #107 | C2×D113 | semidirect |
| 166. #107 | C2×D113 | semidirect |
| 168. #106 | C2×D113 | semidirect |
| 169. #106 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299167 | 2 |
| #20299078 | 2 |
| #20298925 | 2 |
| #20298924 | 2 |
| #20298918 | 2 |
| #20298913 | 2 |
| #20298641 | 2 |
| #20298602 | 2 |
| C2×#16813544 | 2 |
| #20298564 | 2 |
| #427×C113 | 2 |
| #3096 | 113 |