Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
202 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 16. #13133149 | C8 | semidirect |
| 101. C53 | #7127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275458 | 2 |
| #20272546 | 2 |
| C53×#1377 | 2 |
| #7127 | 53 |