Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 80 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×#16811515 | C2 | semidirect |
| 2. #20289717 | C2 | direct (N × H) |
| 6. #16811515 | C22 | semidirect |
| 97. C2×C53 | #1355 | semidirect |
| 109. C53 | C2×#1355 | semidirect |
| 189. C2 | #20289717 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811515 | 2 |
| #20289717 | 2 |
| C2×#16810987 | 2 |
| C2×#1355 | 53 |