Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
766 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 766 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. #20299433 | C2 | semidirect |
| 2. #20299104 | C2 | semidirect |
| 3. #20298789 | C2 | semidirect |
| 4. #20298788 | C2 | semidirect |
| 5. #20298784 | C2 | semidirect |
| 6. #20298570 | C2 | semidirect |
| 7. B(4,𝔽2)×C113 | C2 | semidirect |
| 14. C23×Dic113 | C22 | semidirect |
| 15. #16813606 | C22 | semidirect |
| 16. #16813603 | C22 | semidirect |
| 19. #16813591 | C22 | semidirect |
| 22. #16813578 | C22 | semidirect |
| 23. #16813537 | C22 | semidirect |
| 24. #16813536 | C22 | semidirect |
| 26. #120×C113 | C22 | semidirect |
| 27. #99×C113 | C22 | semidirect |
| 37. C2×Dic226 | D4 | semidirect |
| 42. C2×C22⋊D113 | D4 | semidirect |
| 49. C22×Dic113 | D4 | semidirect |
| 53. C2×C4×D113 | D4 | semidirect |
| 127. C113 | #3025 | semidirect |
| 133. B(4,𝔽2) | D113 | semidirect |
| 148. #120 | C2×D113 | semidirect |
| 154. #99 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299433 | 2 |
| #20299104 | 2 |
| #20298789 | 2 |
| #20298788 | 2 |
| #20298784 | 2 |
| #20298570 | 2 |
| B(4,𝔽2)×C113 | 2 |
| #3025 | 113 |