Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #20289788 | C2 | semidirect |
| 4. #20289782 | C2 | semidirect |
| 17. #16810658 | C4 | semidirect |
| 19. C2×#13133149 | C4 | semidirect |
| 20. #106×D53 | C4 | semidirect |
| 22. C53×#427 | C4 | semidirect |
| 169. #427 | #6157 | semidirect |
| 177. C53 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290952 | 2 |
| #20290597 | 2 |
| #20289788 | 2 |
| #20289782 | 2 |
| #20283307 | 2 |
| #12873 | 53 |