Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
846 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. #20274783 | C2 | semidirect |
| 2. #20272536 | C2 | semidirect |
| 6. #16810378 | C22 | semidirect |
| 21. C22×D4×C53 | C8 | semidirect |
| 158. C53 | #7592 | semidirect |
| 164. C22×D4 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274783 | 2 |
| #20272536 | 2 |
| C2×C53×#390 | 2 |
| #7592 | 53 |