Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 2. C2×#16813692 | C2 | semidirect |
| 3. #20299605 | C2 | semidirect |
| 5. #20299468 | C2 | semidirect |
| 6. #20299463 | C2 | semidirect |
| 23. #16813547 | C4 | semidirect |
| 24. #16813545 | C4 | semidirect |
| 25. #16813543 | C4 | semidirect |
| 26. #102×C113 | C4 | semidirect |
| 110. C113 | #1866 | semidirect |
| 136. #102 | #90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813709 | 2 |
| C2×#16813692 | 2 |
| #20299605 | 2 |
| C2×#16813686 | 2 |
| #20299468 | 2 |
| #20299463 | 2 |
| #20298591 | 2 |
| #1866 | 113 |