Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 114 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. #16811552 | C4 | semidirect |
| 11. #16811551 | C4 | semidirect |
| 17. #16810453 | C4 | semidirect |
| 18. #16810452 | C4 | semidirect |
| 19. C53×#368 | C4 | semidirect |
| 93. #6157 | #368 | direct (N × H) |
| 117. #368 | #6157 | direct (N × H) |
| 121. C53 | C4×#368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#368 | 2 |
| C2×C16×#6157 | 2 |
| #108×#6157 | 2 |
| #20289774 | 2 |
| #368×D53 | 2 |
| C4×#368 | 53 |