Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 10. #16811550 | C4 | semidirect |
| 11. #16811549 | C4 | semidirect |
| 12. C16×#6157 | C4 | semidirect |
| 13. C16×#6157 | C4 | semidirect |
| 17. #16810453 | C4 | semidirect |
| 18. #16810452 | C4 | semidirect |
| 19. C53×#368 | C4 | semidirect |
| 115. #368 | #6157 | semidirect |
| 121. C53 | #12670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291066 | 2 |
| C2×C16×#6157 | 2 |
| #20290520 | 2 |
| #20289778 | 2 |
| #368×D53 | 2 |
| #12670 | 53 |