Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. D4×Dic226 | C2 | semidirect |
| 3. #20298949 | C2 | semidirect |
| 4. #20298940 | C2 | semidirect |
| 5. #20298894 | C2 | semidirect |
| 6. #20298844 | C2 | semidirect |
| 7. #20298804 | C2 | semidirect |
| 8. #20298739 | C2 | semidirect |
| 9. C4×#14268636 | C2 | semidirect |
| 10. #20298608 | C2 | semidirect |
| 11. #436×C113 | C2 | semidirect |
| 127. C113 | #3329 | semidirect |
| 137. #436 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299313 | 2 |
| D4×Dic226 | 2 |
| #20298949 | 2 |
| #20298940 | 2 |
| #20298894 | 2 |
| #20298844 | 2 |
| #20298804 | 2 |
| #20298739 | 2 |
| C4×#14268636 | 2 |
| #20298608 | 2 |
| #436×C113 | 2 |
| #3329 | 113 |