Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 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 |
| 3. #20298948 | C2 | semidirect |
| 4. #20298905 | C2 | semidirect |
| 7. #20298805 | C2 | semidirect |
| 8. Q8×#11744751 | C2 | semidirect |
| 9. C4×#14268637 | C2 | semidirect |
| 116. C113 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299326 | 2 |
| #20298952 | 2 |
| #20298948 | 2 |
| #20298905 | 2 |
| #20298878 | 2 |
| #20298817 | 2 |
| #20298805 | 2 |
| Q8×#11744751 | 2 |
| C4×#14268637 | 2 |
| C4×#14268635 | 2 |
| #556×C113 | 2 |
| #3364 | 113 |