Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#16813649 | C2 | semidirect |
| 2. #20299149 | C2 | semidirect |
| 3. #127×D113 | C2 | semidirect |
| 4. #20298984 | C2 | semidirect |
| 5. #20298975 | C2 | semidirect |
| 6. #20298974 | C2 | semidirect |
| 7. #20298972 | C2 | semidirect |
| 8. C4×#14268630 | C2 | semidirect |
| 9. #492×C113 | C2 | semidirect |
| 14. C2×#14268634 | C22 | semidirect |
| 15. C2×D904 | C22 | semidirect |
| 16. C2×#14268632 | C22 | semidirect |
| 19. #16813619 | C22 | semidirect |
| 22. #16813611 | C22 | semidirect |
| 26. #16813532 | C22 | semidirect |
| 27. C4×#11744751 | C22 | semidirect |
| 28. C2×SD16×C113 | C22 | semidirect |
| 29. C4⋊Q8×C113 | C22 | semidirect |
| 31. C4×C8×C113 | C22 | semidirect |
| 49. #14268630 | D4 | semidirect |
| 85. C8×C113 | C2×D4 | semidirect |
| 86. #11744751 | C2×D4 | semidirect |
| 98. C4×C113 | AGL(1,ℤ/8) | semidirect |
| 109. C113 | #3151 | semidirect |
| 117. #492 | D113 | semidirect |
| 124. C2×SD16 | C2×D113 | semidirect |
| 128. C4⋊Q8 | C2×D113 | semidirect |
| 140. C4×C8 | C2×D113 | semidirect |
| 195. C8 | D4×D113 | semidirect |
| 209. C4 | #16813649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813649 | 2 |
| #20299149 | 2 |
| #127×D113 | 2 |
| #20298984 | 2 |
| #20298975 | 2 |
| #20298974 | 2 |
| #20298972 | 2 |
| C4×#14268630 | 2 |
| #492×C113 | 2 |
| #3151 | 113 |