Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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. #20299134 | C2 | semidirect |
| 2. #20298999 | C2 | semidirect |
| 3. #20298983 | C2 | semidirect |
| 4. #20298954 | C2 | semidirect |
| 6. #20298829 | C2 | semidirect |
| 7. Q16×Dic113 | C2 | semidirect |
| 8. #20298683 | C2 | semidirect |
| 9. #20298680 | C2 | semidirect |
| 10. C2×C8×Dic113 | C2 | semidirect |
| 11. #467×C113 | C2 | semidirect |
| 119. C113 | #3168 | semidirect |
| 124. #467 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299134 | 2 |
| #20298999 | 2 |
| #20298983 | 2 |
| #20298954 | 2 |
| #20298834 | 2 |
| #20298829 | 2 |
| Q16×Dic113 | 2 |
| #20298683 | 2 |
| #20298680 | 2 |
| C2×C8×Dic113 | 2 |
| #467×C113 | 2 |
| #3168 | 113 |