Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
344 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 174. C53 | #10495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285863 | 2 |
| #20275703 | 2 |
| #20273506 | 2 |
| #20273388 | 2 |
| #20273136 | 2 |
| #20272604 | 2 |
| C53×#1561 | 2 |
| #10495 | 53 |