Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #20299226 | C2 | semidirect |
| 3. #20298963 | C2 | semidirect |
| 4. #20298958 | C2 | semidirect |
| 5. #20298953 | C2 | semidirect |
| 6. #20298945 | C2 | semidirect |
| 7. #20298604 | C2 | semidirect |
| 8. #20298600 | C2 | semidirect |
| 9. #20298595 | C2 | semidirect |
| 10. C2×#16813544 | C2 | semidirect |
| 11. #405×C113 | C2 | semidirect |
| 14. #16813622 | C22 | semidirect |
| 17. #16813614 | C22 | semidirect |
| 26. #16813547 | C22 | semidirect |
| 27. #16813547 | C22 | semidirect |
| 28. #16813547 | C22 | semidirect |
| 33. #16813544 | C22 | semidirect |
| 34. #16813544 | C22 | semidirect |
| 35. #16813544 | C22 | semidirect |
| 39. #97×C113 | C22 | semidirect |
| 40. C4×C8×C113 | C22 | semidirect |
| 136. C113 | #3136 | semidirect |
| 147. #405 | D113 | semidirect |
| 175. #97 | C2×D113 | semidirect |
| 176. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299226 | 2 |
| #20299167 | 2 |
| #20298963 | 2 |
| #20298958 | 2 |
| #20298953 | 2 |
| #20298945 | 2 |
| #20298604 | 2 |
| #20298600 | 2 |
| #20298595 | 2 |
| C2×#16813544 | 2 |
| #405×C113 | 2 |
| #3136 | 113 |