Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1126 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1126 conjugacy classes of subgroups — too many to draw. Only its 219 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. C2×#16811353 | C2 | semidirect |
| 3. #20273791 | C2 | direct (N × H) |
| 4. C2×#16810372 | C2 | semidirect |
| 5. C2×#16810355 | C2 | semidirect |
| 10. #16811353 | C22 | semidirect |
| 19. #16810372 | C22 | semidirect |
| 20. #16810355 | C22 | semidirect |
| 86. C2×Dic106 | SD16 | semidirect |
| 134. Dic106 | C2×SD16 | semidirect |
| 159. C2×C53 | #1623 | semidirect |
| 182. C53 | C2×#1623 | semidirect |
| 308. C2 | #20273791 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811353 | 2 |
| C2×#16810820 | 2 |
| #20273791 | 2 |
| C2×#16810372 | 2 |
| C2×#16810355 | 2 |
| C2×C53×#492 | 2 |
| C2×#1623 | 53 |