Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20299318 | C2 | semidirect |
| 3. #20298996 | C2 | semidirect |
| 4. #20298940 | C2 | semidirect |
| 5. #20298923 | C2 | semidirect |
| 6. #20298894 | C2 | semidirect |
| 7. #20298879 | C2 | semidirect |
| 8. #20298827 | C2 | semidirect |
| 9. C4×#14268636 | C2 | semidirect |
| 10. #20298636 | C2 | semidirect |
| 11. C8×D4×C113 | C2 | semidirect |
| 121. C113 | #3340 | semidirect |
| 131. C8×D4 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299318 | 2 |
| #20299313 | 2 |
| #20298996 | 2 |
| #20298940 | 2 |
| #20298923 | 2 |
| #20298894 | 2 |
| #20298879 | 2 |
| #20298827 | 2 |
| C4×#14268636 | 2 |
| #20298636 | 2 |
| C8×D4×C113 | 2 |
| #3340 | 113 |