Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
990 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 170 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. #20291281 | C2 | semidirect |
| 3. #20290415 | C2 | semidirect |
| 4. C2×#16811494 | C2 | semidirect |
| 9. #16811621 | C4 | semidirect |
| 18. #16810529 | C4 | semidirect |
| 19. #16810528 | C4 | semidirect |
| 20. #16810526 | C4 | semidirect |
| 23. C53×#390 | C4 | semidirect |
| 122. #11719936 | C22⋊C4 | semidirect |
| 244. #390 | #6157 | semidirect |
| 249. C53 | #10959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811621 | 2 |
| #20291281 | 2 |
| #20290415 | 2 |
| C2×#16811494 | 2 |
| #20277202 | 2 |
| #10959 | 53 |