Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 87. C2×C8×C53 | Q16 | semidirect |
| 195. C53 | #9048 | semidirect |
| 260. C2×C8 | #11719925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284754 | 2 |
| #20283655 | 2 |
| #20273373 | 2 |
| #20273144 | 2 |
| #20272612 | 2 |
| #20272560 | 2 |
| C53×#1985 | 2 |
| #9048 | 53 |