Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
372 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20290264 | C2 | semidirect |
| 2. C2×#16811486 | C2 | semidirect |
| 4. #20289561 | C2 | semidirect |
| 178. C53 | #8606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290264 | 2 |
| C2×#16811486 | 2 |
| #20290012 | 2 |
| #20289561 | 2 |
| #20283358 | 2 |
| #8606 | 53 |