Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
464 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 168 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. #20299633 | C2 | semidirect |
| 2. #20299629 | C2 | semidirect |
| 3. D4×#11744753 | C2 | semidirect |
| 4. #20299619 | C2 | semidirect |
| 5. #20299615 | C2 | semidirect |
| 6. #20299568 | C2 | semidirect |
| 7. C2×C22⋊#11744753 | C2 | semidirect |
| 9. C2×#14268656 | C22 | semidirect |
| 10. C22×#11744753 | C22 | semidirect |
| 11. #16813689 | C22 | semidirect |
| 12. C4⋊#11744753 | C22 | semidirect |
| 16. C22⋊#11744753 | C22 | semidirect |
| 17. C22⋊#11744753 | C22 | semidirect |
| 18. #16813677 | C22 | semidirect |
| 19. C4×#11744753 | C22 | semidirect |
| 69. D4×C113 | M16 | semidirect |
| 115. C113 | #2974 | semidirect |
| 184. D4 | #14268656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299633 | 2 |
| #20299629 | 2 |
| D4×#11744753 | 2 |
| #20299619 | 2 |
| #20299615 | 2 |
| #20299568 | 2 |
| C2×C22⋊#11744753 | 2 |
| C2×D4×Dic113 | 2 |
| #2974 | 113 |