Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
382 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 112 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. #20290934 | C2 | semidirect |
| 4. #20289768 | C2 | semidirect |
| 10. #16811520 | C4 | semidirect |
| 11. #16811519 | C4 | semidirect |
| 18. C2×#13133157 | C4 | semidirect |
| 19. C2×#13133156 | C4 | semidirect |
| 21. C2×C16×D53 | C4 | semidirect |
| 23. C22×C16×C53 | C4 | semidirect |
| 148. C22×C16 | #6157 | semidirect |
| 157. C53 | #12617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290952 | 2 |
| #20290934 | 2 |
| #20290470 | 2 |
| #20289768 | 2 |
| C2×#16811039 | 2 |
| #12617 | 53 |