Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
488 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. C22×#13133157 | C2 | semidirect |
| 2. C2×#16810430 | C2 | semidirect |
| 3. #20274753 | C2 | semidirect |
| 4. #20272810 | C2 | semidirect |
| 25. C2×#11719908 | D4 | semidirect |
| 158. C53 | #13064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133157 | 2 |
| C2×#16810430 | 2 |
| #20274753 | 2 |
| #20272810 | 2 |
| C53×#3050 | 2 |
| #13064 | 53 |