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×#16813670 | C2 | semidirect |
| 2. C2×#16813642 | C2 | semidirect |
| 3. #20299176 | C2 | semidirect |
| 4. #20298759 | C2 | semidirect |
| 5. #20298752 | C2 | semidirect |
| 6. #20298742 | C2 | semidirect |
| 7. #20298735 | C2 | semidirect |
| 8. #20298600 | C2 | semidirect |
| 9. C2×#16813546 | C2 | semidirect |
| 10. #20298566 | C2 | semidirect |
| 11. C2×#137×C113 | C2 | semidirect |
| 52. #14268647 | D4 | semidirect |
| 86. C2×Q8×C113 | D4 | semidirect |
| 170. C113 | #3013 | semidirect |
| 172. C2×#137 | D113 | semidirect |
| 233. C2×Q8 | C22⋊D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813670 | 2 |
| C2×#16813642 | 2 |
| #20299176 | 2 |
| #20298759 | 2 |
| #20298752 | 2 |
| #20298742 | 2 |
| #20298735 | 2 |
| #20298600 | 2 |
| C2×#16813546 | 2 |
| #20298566 | 2 |
| C2×#137×C113 | 2 |
| #3013 | 113 |