Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
448 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 103 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×C22⋊#11719908 | C2 | semidirect |
| 3. #20272729 | C2 | semidirect |
| 4. C53×#1810 | C2 | semidirect |
| 15. C22⋊#11719908 | C22 | semidirect |
| 19. C53×#341 | C22 | semidirect |
| 146. #1810 | D53 | semidirect |
| 169. #341 | C2×D53 | semidirect |
| 170. C53 | #11891 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810859 | 2 |
| C2×C22⋊#11719908 | 2 |
| #20272729 | 2 |
| C53×#1810 | 2 |
| #11891 | 53 |