Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. #20290930 | C2 | semidirect |
| 4. #20290536 | C2 | semidirect |
| 5. #20289793 | C2 | semidirect |
| 6. #20289784 | C2 | semidirect |
| 19. #16811538 | C4 | semidirect |
| 26. #16810439 | C4 | semidirect |
| 27. #16810437 | C4 | semidirect |
| 28. #16810435 | C4 | semidirect |
| 29. C53×#362 | C4 | semidirect |
| 189. #362 | #6157 | semidirect |
| 196. C53 | #12651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811669 | 2 |
| #20291031 | 2 |
| #20290930 | 2 |
| #20290536 | 2 |
| #20289793 | 2 |
| #20289784 | 2 |
| #20276463 | 2 |
| #12651 | 53 |