Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
604 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 4. #16811568 | C4 | semidirect |
| 5. #16811567 | C4 | semidirect |
| 14. #16810646 | C4 | semidirect |
| 16. C4×#11719917 | C4 | semidirect |
| 17. C4×M16×C53 | C4 | semidirect |
| 128. C4×M16 | #6157 | semidirect |
| 136. C53 | #8050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291162 | 2 |
| #20289595 | 2 |
| #20283346 | 2 |
| #8050 | 53 |