Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 199. C53 | #8774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277675 | 2 |
| C4×#13133135 | 2 |
| #20273058 | 2 |
| #20272609 | 2 |
| #20272607 | 2 |
| #20272579 | 2 |
| C53×#1288 | 2 |
| #8774 | 53 |