Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#14268636 | C2 | semidirect |
| 2. C22×#14268630 | C2 | semidirect |
| 3. C2×#16813602 | C2 | semidirect |
| 5. #20298845 | C2 | direct (N × H) |
| 6. C2×#16813545 | C2 | semidirect |
| 7. C2×#16813542 | C2 | semidirect |
| 8. C2×#107×C113 | C2 | semidirect |
| 14. C2×#14268636 | C22 | semidirect |
| 16. C2×#14268630 | C22 | semidirect |
| 19. #16813602 | C22 | semidirect |
| 25. #16813545 | C22 | semidirect |
| 26. #16813542 | C22 | semidirect |
| 30. #107×C113 | C22 | semidirect |
| 59. C2×C8×C113 | D4 | semidirect |
| 96. C8×C113 | C2×D4 | semidirect |
| 117. C2×C113 | #468 | semidirect |
| 124. C113 | C2×#468 | semidirect |
| 130. C2×#107 | D113 | semidirect |
| 152. #107 | C2×D113 | semidirect |
| 180. C2×C8 | D452 | semidirect |
| 221. C8 | C2×D452 | semidirect |
| 243. C2 | #20298845 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268636 | 2 |
| C22×#14268630 | 2 |
| C2×#16813602 | 2 |
| C2×#16813597 | 2 |
| #20298845 | 2 |
| C2×#16813545 | 2 |
| C2×#16813542 | 2 |
| C2×#107×C113 | 2 |
| C2×#468 | 113 |