Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
368 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 178. C53 | #9374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283810 | 2 |
| #20273415 | 2 |
| #20273353 | 2 |
| #20273118 | 2 |
| #20272584 | 2 |
| #20272576 | 2 |
| C53×#3237 | 2 |
| #9374 | 53 |