Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20298993 | C2 | semidirect |
| 4. #20298992 | C2 | semidirect |
| 5. #20298960 | C2 | semidirect |
| 6. #20298823 | C2 | semidirect |
| 7. #20298819 | C2 | semidirect |
| 8. #20298755 | C2 | semidirect |
| 10. #20298653 | C2 | semidirect |
| 11. #489×C113 | C2 | semidirect |
| 14. C2×Dic452 | C22 | semidirect |
| 15. C2×#14268637 | C22 | semidirect |
| 18. #16813622 | C22 | semidirect |
| 28. #16813587 | C22 | semidirect |
| 33. #16813551 | C22 | semidirect |
| 34. #16813545 | C22 | semidirect |
| 37. #16813533 | C22 | semidirect |
| 38. C4⋊Q8×C113 | C22 | semidirect |
| 40. #103×C113 | C22 | semidirect |
| 42. #97×C113 | C22 | semidirect |
| 143. C113 | #3215 | semidirect |
| 149. #489 | D113 | semidirect |
| 162. C4⋊Q8 | C2×D113 | semidirect |
| 180. #103 | C2×D113 | semidirect |
| 185. #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 |
| #20298993 | 2 |
| #20298992 | 2 |
| #20298960 | 2 |
| #20298823 | 2 |
| #20298819 | 2 |
| #20298755 | 2 |
| #20298750 | 2 |
| #20298653 | 2 |
| #489×C113 | 2 |
| #3215 | 113 |