Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#16813669 | C2 | semidirect |
| 2. C2×#16813655 | C2 | semidirect |
| 3. C2×#16813642 | C2 | semidirect |
| 4. #20299179 | C2 | semidirect |
| 5. #20298761 | C2 | semidirect |
| 6. #20298755 | C2 | semidirect |
| 7. #20298744 | C2 | semidirect |
| 8. #20298738 | C2 | semidirect |
| 9. C2×#16813545 | C2 | semidirect |
| 10. #20298566 | C2 | semidirect |
| 11. #417×C113 | C2 | semidirect |
| 58. C2×Dic226 | D4 | semidirect |
| 87. #41×C113 | D4 | semidirect |
| 170. C113 | #3013 | semidirect |
| 179. #417 | D113 | semidirect |
| 224. #41 | D452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813669 | 2 |
| C2×#16813655 | 2 |
| C2×#16813642 | 2 |
| #20299179 | 2 |
| #20298761 | 2 |
| #20298755 | 2 |
| #20298744 | 2 |
| #20298738 | 2 |
| C2×#16813545 | 2 |
| #20298566 | 2 |
| #417×C113 | 2 |
| #3013 | 113 |