Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 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×#16813650 | C2 | semidirect |
| 2. #20299148 | C2 | semidirect |
| 3. C2×C4×D452 | C2 | semidirect |
| 4. #20298814 | C2 | semidirect |
| 5. #20298804 | C2 | semidirect |
| 6. #20298794 | C2 | semidirect |
| 7. #20298600 | C2 | semidirect |
| 8. #423×C113 | C2 | semidirect |
| 15. #16813622 | C22 | semidirect |
| 16. #16813619 | C22 | semidirect |
| 17. #16813610 | C22 | semidirect |
| 28. #16813547 | C22 | semidirect |
| 29. #16813544 | C22 | semidirect |
| 32. C4⋊C8×C113 | C22 | semidirect |
| 33. C4⋊C8×C113 | C22 | semidirect |
| 42. C2×D452 | D4 | semidirect |
| 118. C4×C113 | AGL(1,ℤ/8) | semidirect |
| 130. C113 | #3036 | semidirect |
| 137. #423 | D113 | semidirect |
| 160. C4⋊C8 | C2×D113 | semidirect |
| 161. C4⋊C8 | C2×D113 | semidirect |
| 250. C4 | #16813650 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813650 | 2 |
| #20299148 | 2 |
| C2×C4×D452 | 2 |
| #20298814 | 2 |
| #20298804 | 2 |
| #20298794 | 2 |
| #20298600 | 2 |
| #423×C113 | 2 |
| #3036 | 113 |