Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
236 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 37. C2×Dic106 | C16 | semidirect |
| 118. C53 | #7128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275651 | 2 |
| #20272793 | 2 |
| C53×#1374 | 2 |
| #7128 | 53 |