Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20298961 | C2 | semidirect |
| 4. #20298946 | C2 | semidirect |
| 5. #20298945 | C2 | semidirect |
| 6. #20298944 | C2 | semidirect |
| 7. #20298601 | C2 | semidirect |
| 8. C4×#14268630 | C2 | semidirect |
| 9. #486×C113 | C2 | semidirect |
| 14. #16813622 | C22 | semidirect |
| 19. #16813613 | C22 | semidirect |
| 26. #16813544 | C22 | semidirect |
| 27. #16813543 | C22 | semidirect |
| 28. #16813542 | C22 | semidirect |
| 29. #16813532 | C22 | semidirect |
| 30. C4×#11744751 | C22 | semidirect |
| 31. C4⋊Q8×C113 | C22 | semidirect |
| 33. #102×C113 | C22 | semidirect |
| 34. C4×C8×C113 | C22 | semidirect |
| 124. C113 | #3138 | semidirect |
| 131. #486 | D113 | semidirect |
| 139. C4⋊Q8 | C2×D113 | semidirect |
| 155. #102 | C2×D113 | semidirect |
| 158. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299153 | 2 |
| #127×D113 | 2 |
| #20298961 | 2 |
| #20298946 | 2 |
| #20298945 | 2 |
| #20298944 | 2 |
| #20298601 | 2 |
| C4×#14268630 | 2 |
| #486×C113 | 2 |
| #3138 | 113 |