Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1170 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 171 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. #20274477 | C2 | semidirect |
| 2. C2×#16810363 | C2 | semidirect |
| 5. C2×#13133128 | C22 | semidirect |
| 142. C22×C53 | #329 | semidirect |
| 175. C53 | #8334 | semidirect |
| 301. C22 | #16810363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274477 | 2 |
| C2×#16810363 | 2 |
| C22×#124×C53 | 2 |
| #8334 | 53 |