Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20299148 | C2 | semidirect |
| 2. #20298916 | C2 | semidirect |
| 3. #20298888 | C2 | semidirect |
| 4. #20298793 | C2 | semidirect |
| 5. #20298732 | C2 | semidirect |
| 6. #20298708 | C2 | semidirect |
| 7. #20298655 | C2 | semidirect |
| 8. C2×C4×D4×C113 | C2 | semidirect |
| 11. #16813622 | C22 | semidirect |
| 12. #16813619 | C22 | semidirect |
| 17. C4×D452 | C22 | semidirect |
| 18. #16813553 | C22 | semidirect |
| 19. C4⋊#11744751 | C22 | semidirect |
| 21. #16813542 | C22 | semidirect |
| 23. #16813533 | C22 | semidirect |
| 73. D4×C113 | #41 | semidirect |
| 121. C113 | #3109 | semidirect |
| 123. C2×C4×D4 | D113 | semidirect |
| 199. D4 | #14268647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299148 | 2 |
| #20298916 | 2 |
| #20298888 | 2 |
| #20298793 | 2 |
| #20298732 | 2 |
| #20298708 | 2 |
| #20298655 | 2 |
| C2×C4×D4×C113 | 2 |
| #3109 | 113 |