Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. #20291067 | C2 | semidirect |
| 4. #20289787 | C2 | semidirect |
| 19. #16810405 | C4 | semidirect |
| 20. #16810404 | C4 | semidirect |
| 21. C53×#349 | C4 | semidirect |
| 50. #13133157 | C2×C4 | semidirect |
| 54. M32×C53 | C2×C4 | semidirect |
| 185. #349 | #6157 | semidirect |
| 187. C53 | #12923 | semidirect |
| 210. M32 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291368 | 2 |
| #20291067 | 2 |
| #20290593 | 2 |
| #20289787 | 2 |
| #349×D53 | 2 |
| #12923 | 53 |