Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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. #20299204 | C2 | direct (N × H) |
| 2. C2×#16813619 | C2 | semidirect |
| 3. C2×#16813607 | C2 | semidirect |
| 4. C2×#16813597 | C2 | semidirect |
| 5. C2×#16813597 | C2 | semidirect |
| 6. C2×#16813584 | C2 | semidirect |
| 7. C2×#16813579 | C2 | semidirect |
| 8. C2×#125×C113 | C2 | semidirect |
| 14. #16813619 | C22 | semidirect |
| 15. #16813607 | C22 | semidirect |
| 16. #16813597 | C22 | semidirect |
| 17. #16813597 | C22 | semidirect |
| 18. #16813584 | C22 | semidirect |
| 19. #16813579 | C22 | semidirect |
| 25. #125×C113 | C22 | semidirect |
| 92. C2×C113 | #540 | semidirect |
| 98. C113 | C2×#540 | semidirect |
| 101. C2×#125 | D113 | semidirect |
| 113. #125 | C2×D113 | semidirect |
| 192. C2 | #20299204 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299204 | 2 |
| C2×#16813619 | 2 |
| C2×#16813607 | 2 |
| C2×#16813597 | 2 |
| C2×#16813584 | 2 |
| C2×#16813579 | 2 |
| C2×#125×C113 | 2 |
| C2×#540 | 113 |