Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×#16810453 | C2 | semidirect |
| 3. #20272909 | C2 | semidirect |
| 4. #20272906 | C2 | semidirect |
| 5. C2×C53×M64 | C2 | semidirect |
| 109. C2×M64 | D53 | semidirect |
| 133. C53 | #13625 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811055 | 2 |
| C2×#16810453 | 2 |
| #20272909 | 2 |
| #20272906 | 2 |
| C2×C53×M64 | 2 |
| #13625 | 53 |