Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
230 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 9. #16811485 | C4 | semidirect |
| 12. C4⋊#11719908 | C4 | semidirect |
| 14. C53×C4⋊C16 | C4 | semidirect |
| 112. C4⋊C16 | #6157 | semidirect |
| 115. C53 | #7279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290652 | 2 |
| #20290265 | 2 |
| #20276469 | 2 |
| #7279 | 53 |