Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20299132 | C2 | semidirect |
| 2. #20298980 | C2 | semidirect |
| 3. #20298952 | C2 | semidirect |
| 4. #20298805 | C2 | semidirect |
| 5. #20298800 | C2 | semidirect |
| 6. #20298795 | C2 | semidirect |
| 7. #20298790 | C2 | semidirect |
| 8. #20298760 | C2 | semidirect |
| 9. #20298743 | C2 | semidirect |
| 10. #20298651 | C2 | semidirect |
| 11. #532×C113 | C2 | semidirect |
| 145. C113 | #3212 | semidirect |
| 146. #532 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299132 | 2 |
| #20298980 | 2 |
| #20298952 | 2 |
| #20298805 | 2 |
| #20298800 | 2 |
| #20298795 | 2 |
| #20298790 | 2 |
| #20298760 | 2 |
| #20298743 | 2 |
| #20298651 | 2 |
| #532×C113 | 2 |
| #3212 | 113 |