Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20299153 | C2 | semidirect |
| 3. #20298904 | C2 | semidirect |
| 4. #20298896 | C2 | semidirect |
| 5. #20298894 | C2 | semidirect |
| 6. #20298888 | C2 | semidirect |
| 7. #20298880 | C2 | semidirect |
| 8. #20298635 | C2 | semidirect |
| 9. C4⋊C8×D113 | C2 | semidirect |
| 11. #474×C113 | C2 | semidirect |
| 44. #14268646 | Q8 | semidirect |
| 135. C113 | #3076 | semidirect |
| 143. #474 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299153 | 2 |
| C4×#14268646 | 2 |
| #20298904 | 2 |
| #20298896 | 2 |
| #20298894 | 2 |
| #20298888 | 2 |
| #20298880 | 2 |
| #20298635 | 2 |
| C4⋊C8×D113 | 2 |
| #20298591 | 2 |
| #474×C113 | 2 |
| #3076 | 113 |