Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16810449 | C2 | semidirect |
| 3. #20272897 | C2 | semidirect |
| 4. #20272894 | C2 | semidirect |
| 5. C2×C53×M64 | C2 | semidirect |
| 8. #16811055 | C4 | semidirect |
| 26. Dic424 | C2×C4 | semidirect |
| 29. D848 | C2×C4 | semidirect |
| 92. C2×M64 | D53 | semidirect |
| 113. C53 | #13616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811055 | 2 |
| C2×#16810449 | 2 |
| #20272897 | 2 |
| #20272894 | 2 |
| C2×C53×M64 | 2 |
| #13616 | 53 |