Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
310 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 28. C4×#88322 | C8 | semidirect |
| 122. C53 | #8780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274402 | 2 |
| #20273461 | 2 |
| #20272559 | 2 |
| #20272544 | 2 |
| C53×#1274 | 2 |
| #8780 | 53 |