Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20299412 | C2 | semidirect |
| 2. #20299411 | C2 | semidirect |
| 3. #20299041 | C2 | semidirect |
| 4. #20299040 | C2 | semidirect |
| 5. #20299037 | C2 | semidirect |
| 6. #20299029 | C2 | semidirect |
| 7. #20299028 | C2 | semidirect |
| 8. C2×#16813568 | C2 | semidirect |
| 9. Q32×D113 | C2 | semidirect |
| 10. #20299016 | C2 | semidirect |
| 11. #510×C113 | C2 | semidirect |
| 124. C113 | #3417 | semidirect |
| 130. #510 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299412 | 2 |
| #20299411 | 2 |
| #20299041 | 2 |
| #20299040 | 2 |
| #20299037 | 2 |
| #20299029 | 2 |
| #20299028 | 2 |
| C2×#16813568 | 2 |
| Q32×D113 | 2 |
| #20299016 | 2 |
| #510×C113 | 2 |
| #3417 | 113 |