Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 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. #20299153 | C2 | semidirect |
| 3. #20298960 | C2 | semidirect |
| 4. #20298958 | C2 | semidirect |
| 5. #20298957 | C2 | semidirect |
| 6. #20298954 | C2 | semidirect |
| 7. #20298951 | C2 | semidirect |
| 8. #20298605 | C2 | semidirect |
| 10. #20298550 | C2 | semidirect |
| 11. #489×C113 | C2 | semidirect |
| 15. #16813622 | C22 | semidirect |
| 16. #16813613 | C22 | semidirect |
| 30. #16813547 | C22 | semidirect |
| 31. #16813546 | C22 | semidirect |
| 32. #16813545 | C22 | semidirect |
| 36. #16813533 | C22 | semidirect |
| 37. C8×Dic113 | C22 | semidirect |
| 38. C4⋊Q8×C113 | C22 | semidirect |
| 40. #103×C113 | C22 | semidirect |
| 42. #97×C113 | C22 | semidirect |
| 139. C113 | #3140 | semidirect |
| 145. #489 | D113 | semidirect |
| 155. C4⋊Q8 | C2×D113 | semidirect |
| 174. #103 | C2×D113 | semidirect |
| 180. #97 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299153 | 2 |
| #124×D113 | 2 |
| #20298960 | 2 |
| #20298958 | 2 |
| #20298957 | 2 |
| #20298954 | 2 |
| #20298951 | 2 |
| #20298605 | 2 |
| #20298601 | 2 |
| #20298550 | 2 |
| #489×C113 | 2 |
| #3140 | 113 |