Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20299203 | C2 | semidirect |
| 2. #20298988 | C2 | semidirect |
| 3. #20298972 | C2 | semidirect |
| 4. #20298966 | C2 | semidirect |
| 5. #20298952 | C2 | semidirect |
| 6. #20298810 | C2 | semidirect |
| 7. #20298800 | C2 | semidirect |
| 8. #20298743 | C2 | semidirect |
| 9. #20298737 | C2 | semidirect |
| 10. #20298659 | C2 | semidirect |
| 11. #536×C113 | C2 | semidirect |
| 121. C113 | #3221 | semidirect |
| 123. #536 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299203 | 2 |
| #20298988 | 2 |
| #20298972 | 2 |
| #20298966 | 2 |
| #20298952 | 2 |
| #20298810 | 2 |
| #20298800 | 2 |
| #20298743 | 2 |
| #20298737 | 2 |
| #20298659 | 2 |
| #536×C113 | 2 |
| #3221 | 113 |