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 |
|---|---|---|
| 2. #20298964 | C2 | semidirect |
| 3. #20298960 | C2 | semidirect |
| 4. #20298955 | C2 | semidirect |
| 5. #20298946 | C2 | semidirect |
| 6. #20298602 | C2 | semidirect |
| 7. #20298597 | C2 | semidirect |
| 8. #20298592 | C2 | semidirect |
| 9. C2×#16813542 | C2 | semidirect |
| 10. #20298554 | C2 | semidirect |
| 11. #544×C113 | C2 | semidirect |
| 21. #16813545 | C22 | semidirect |
| 22. #16813545 | C22 | semidirect |
| 23. #16813545 | C22 | semidirect |
| 28. #16813542 | C22 | semidirect |
| 29. #16813542 | C22 | semidirect |
| 30. #16813542 | C22 | semidirect |
| 31. #16813533 | C22 | semidirect |
| 32. C4×#11744751 | C22 | semidirect |
| 34. C4⋊Q8×C113 | C22 | semidirect |
| 36. #125×C113 | C22 | semidirect |
| 136. C113 | #3136 | semidirect |
| 137. #544 | D113 | semidirect |
| 153. C4⋊Q8 | C2×D113 | semidirect |
| 156. #125 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299167 | 2 |
| #20298964 | 2 |
| #20298960 | 2 |
| #20298955 | 2 |
| #20298946 | 2 |
| #20298602 | 2 |
| #20298597 | 2 |
| #20298592 | 2 |
| C2×#16813542 | 2 |
| #20298554 | 2 |
| #544×C113 | 2 |
| #3136 | 113 |