Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
854 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 854 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. #20275892 | C2 | semidirect |
| 2. #20275879 | C2 | semidirect |
| 5. #16811249 | C22 | semidirect |
| 9. #16810390 | C22 | semidirect |
| 10. #16810389 | C22 | semidirect |
| 20. C25×C53 | Q8 | semidirect |
| 24. C22×D4×C53 | Q8 | semidirect |
| 26. C23×C4×C53 | Q8 | semidirect |
| 139. C53 | #32873 | semidirect |
| 140. C25 | Dic106 | semidirect |
| 144. C22×D4 | Dic106 | semidirect |
| 146. C23×C4 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275892 | 2 |
| #20275879 | 2 |
| #20274630 | 2 |
| C53×#1781 | 2 |
| #32873 | 53 |