Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20299318 | C2 | semidirect |
| 2. #20299305 | C2 | semidirect |
| 3. #20298951 | C2 | semidirect |
| 4. #20298949 | C2 | semidirect |
| 5. #20298904 | C2 | semidirect |
| 6. #20298888 | C2 | semidirect |
| 8. #20298803 | C2 | semidirect |
| 9. C8×Dic226 | C2 | semidirect |
| 10. #20298689 | C2 | semidirect |
| 121. C113 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299318 | 2 |
| #20299305 | 2 |
| #20298951 | 2 |
| #20298949 | 2 |
| #20298904 | 2 |
| #20298888 | 2 |
| #20298811 | 2 |
| #20298803 | 2 |
| C8×Dic226 | 2 |
| #20298689 | 2 |
| C4×D8×C113 | 2 |
| #3360 | 113 |