Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 92 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. #20289786 | C2 | semidirect |
| 4. #20289786 | C2 | semidirect |
| 14. #16810661 | C4 | semidirect |
| 19. #107×D53 | C4 | semidirect |
| 20. #107×D53 | C4 | semidirect |
| 22. C53×#427 | C4 | semidirect |
| 170. #427 | #6157 | semidirect |
| 179. C53 | #12870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290943 | 2 |
| #20290591 | 2 |
| #20289786 | 2 |
| #427×D53 | 2 |
| #12870 | 53 |