Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
540 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 15. #16811483 | C4 | semidirect |
| 18. #16810372 | C4 | semidirect |
| 19. #16810371 | C4 | semidirect |
| 20. C53×#333 | C4 | semidirect |
| 121. #6157 | #333 | direct (N × H) |
| 154. #333 | #6157 | direct (N × H) |
| 155. C53 | C4×#333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×#6157 | 2 |
| C4⋊C8×#6157 | 2 |
| D53⋊#333 | 2 |
| #20289594 | 2 |
| #333×D53 | 2 |
| C4×#333 | 53 |