Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
356 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 356 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 |
|---|---|---|
| 25. #13133151 | Q8 | semidirect |
| 35. M32×C53 | Q8 | semidirect |
| 111. C53 | #13457 | semidirect |
| 123. M32 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811021 | 2 |
| C2×#16810446 | 2 |
| #20275463 | 2 |
| #20272821 | 2 |
| C53×#1376 | 2 |
| #13457 | 53 |