Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20299326 | C2 | semidirect |
| 2. #20298952 | C2 | semidirect |
| 4. #20298898 | C2 | semidirect |
| 5. #20298883 | C2 | semidirect |
| 6. #20298817 | C2 | semidirect |
| 8. Q8×#11744751 | C2 | semidirect |
| 9. C4×#14268637 | C2 | semidirect |
| 10. C4×#14268635 | C2 | semidirect |
| 118. C113 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299326 | 2 |
| #20298952 | 2 |
| #20298944 | 2 |
| #20298898 | 2 |
| #20298883 | 2 |
| #20298817 | 2 |
| #20298795 | 2 |
| Q8×#11744751 | 2 |
| C4×#14268637 | 2 |
| C4×#14268635 | 2 |
| #559×C113 | 2 |
| #3365 | 113 |