Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic226 | C2 | semidirect |
| 3. #20298949 | C2 | semidirect |
| 4. #20298929 | C2 | semidirect |
| 5. #20298884 | C2 | semidirect |
| 6. #20298827 | C2 | semidirect |
| 7. #20298804 | C2 | semidirect |
| 8. #20298739 | C2 | semidirect |
| 9. C4×#14268636 | C2 | semidirect |
| 10. C2×#16813547 | C2 | semidirect |
| 11. C8×D4×C113 | C2 | semidirect |
| 79. D4×C113 | SD16 | semidirect |
| 102. Dic226 | #41 | semidirect |
| 129. C113 | #3298 | semidirect |
| 139. C8×D4 | D113 | semidirect |
| 217. D4 | #14268636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic226 | 2 |
| #20299252 | 2 |
| #20298949 | 2 |
| #20298929 | 2 |
| #20298884 | 2 |
| #20298827 | 2 |
| #20298804 | 2 |
| #20298739 | 2 |
| C4×#14268636 | 2 |
| C2×#16813547 | 2 |
| C8×D4×C113 | 2 |
| #3298 | 113 |