Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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. C4⋊Q8×D113 | C2 | semidirect |
| 3. #20298993 | C2 | semidirect |
| 4. #20298967 | C2 | semidirect |
| 5. #20298966 | C2 | semidirect |
| 6. #20298806 | C2 | semidirect |
| 7. #20298801 | C2 | semidirect |
| 8. #20298752 | C2 | semidirect |
| 10. #20298653 | C2 | semidirect |
| 11. #497×C113 | C2 | semidirect |
| 136. C113 | #3218 | semidirect |
| 140. #497 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D113 | 2 |
| #20299127 | 2 |
| #20298993 | 2 |
| #20298967 | 2 |
| #20298966 | 2 |
| #20298806 | 2 |
| #20298801 | 2 |
| #20298752 | 2 |
| #20298735 | 2 |
| #20298653 | 2 |
| #497×C113 | 2 |
| #3218 | 113 |