Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
426 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 120. #88322 | #101 | semidirect |
| 164. C53 | #9794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811019 | 2 |
| #20275703 | 2 |
| #20275560 | 2 |
| #20273470 | 2 |
| #20273399 | 2 |
| #20272996 | 2 |
| C53×#1546 | 2 |
| #9794 | 53 |