Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
338 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 38. #13133149 | Q8 | semidirect |
| 44. M32×C53 | Q8 | semidirect |
| 140. C53 | #13454 | semidirect |
| 156. M32 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285239 | 2 |
| #20276503 | 2 |
| #20275458 | 2 |
| #20272821 | 2 |
| C53×#1377 | 2 |
| #13454 | 53 |