Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
422 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 152 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. #20299629 | C2 | semidirect |
| 2. #20299627 | C2 | semidirect |
| 3. #20299625 | C2 | semidirect |
| 4. D4×#11744753 | C2 | semidirect |
| 5. #20299622 | C2 | semidirect |
| 6. #20299572 | C2 | semidirect |
| 7. #20299571 | C2 | semidirect |
| 8. C2×C22⋊#11744753 | C2 | semidirect |
| 10. C2×#14268657 | C22 | semidirect |
| 11. C2×#14268656 | C22 | semidirect |
| 12. C2×#14268655 | C22 | semidirect |
| 15. C22×#11744753 | C22 | semidirect |
| 16. #16813689 | C22 | semidirect |
| 17. C4⋊#11744753 | C22 | semidirect |
| 18. #16813679 | C22 | semidirect |
| 23. C22⋊#11744753 | C22 | semidirect |
| 24. #16813677 | C22 | semidirect |
| 25. C4×#11744753 | C22 | semidirect |
| 133. C113 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299629 | 2 |
| #20299627 | 2 |
| #20299625 | 2 |
| D4×#11744753 | 2 |
| #20299622 | 2 |
| #20299572 | 2 |
| #20299571 | 2 |
| C2×C22⋊#11744753 | 2 |
| #20299104 | 2 |
| #2977 | 113 |