Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20274753 | C2 | semidirect |
| 3. #20272731 | C2 | semidirect |
| 4. C53×#2112 | C2 | semidirect |
| 15. #16810388 | C22 | semidirect |
| 19. C53×C22⋊C16 | C22 | semidirect |
| 145. #2112 | D53 | semidirect |
| 168. C22⋊C16 | C2×D53 | semidirect |
| 170. C53 | #11895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810859 | 2 |
| #20274753 | 2 |
| #20272731 | 2 |
| C53×#2112 | 2 |
| #11895 | 53 |