Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #20299678 | C2 | semidirect |
| 2. #20299644 | C2 | semidirect |
| 3. #20299642 | C2 | semidirect |
| 4. D113⋊#108 | C2 | semidirect |
| 5. #20299597 | C2 | semidirect |
| 6. #20299561 | C2 | semidirect |
| 9. #16813710 | C22 | semidirect |
| 14. #16813693 | C22 | semidirect |
| 15. #16813692 | C22 | semidirect |
| 16. #16813687 | C22 | semidirect |
| 17. #16813676 | C22 | semidirect |
| 18. C8×#90673 | C22 | semidirect |
| 20. #16813645 | C4 | semidirect |
| 21. #16813645 | C4 | semidirect |
| 24. C2×#14268634 | C4 | semidirect |
| 25. C2×D904 | C4 | semidirect |
| 27. C2×Q16×C113 | C4 | semidirect |
| 102. C113 | #2957 | semidirect |
| 115. C2×Q16 | #90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299678 | 2 |
| #20299644 | 2 |
| #20299642 | 2 |
| D113⋊#108 | 2 |
| #20299597 | 2 |
| #20299561 | 2 |
| C2×#16813645 | 2 |
| #2957 | 113 |