Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1128 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 340 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. #20291682 | C2 | semidirect |
| 2. #20290953 | C2 | semidirect |
| 3. C2×#16811520 | C2 | semidirect |
| 6. C2×#13133291 | C22 | semidirect |
| 8. #16811520 | C22 | semidirect |
| 142. C53 | #33337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291682 | 2 |
| #20290953 | 2 |
| C2×#16811520 | 2 |
| C2×#16811388 | 2 |
| #33337 | 53 |