Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×Dic226 | C2 | semidirect |
| 3. #20298945 | C2 | semidirect |
| 4. #20298943 | C2 | semidirect |
| 5. #20298888 | C2 | semidirect |
| 6. #20298887 | C2 | semidirect |
| 7. #20298798 | C2 | semidirect |
| 8. #20298796 | C2 | semidirect |
| 9. C8×Dic226 | C2 | semidirect |
| 10. #20298683 | C2 | semidirect |
| 11. C4×SD16×C113 | C2 | semidirect |
| 77. Q8×C113 | #41 | semidirect |
| 99. Dic226 | SD16 | semidirect |
| 126. C113 | #3362 | semidirect |
| 137. C4×SD16 | D113 | semidirect |
| 206. Q8 | #14268647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic226 | 2 |
| #20299269 | 2 |
| #20298945 | 2 |
| #20298943 | 2 |
| #20298888 | 2 |
| #20298887 | 2 |
| #20298798 | 2 |
| #20298796 | 2 |
| C8×Dic226 | 2 |
| #20298683 | 2 |
| C4×SD16×C113 | 2 |
| #3362 | 113 |