Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1038 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 1038 conjugacy classes of subgroups — too many to draw. Only its 172 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. C2×#16811519 | C2 | semidirect |
| 2. #20290942 | C2 | semidirect |
| 4. C2×#13133291 | C22 | semidirect |
| 120. C22×C53 | #349 | semidirect |
| 146. C53 | #12681 | semidirect |
| 252. C22 | #16811519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811519 | 2 |
| #20290942 | 2 |
| C23×#11719917 | 2 |
| #12681 | 53 |