Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 10. #16811025 | C4 | semidirect |
| 11. #16811021 | C4 | semidirect |
| 49. M32×C53 | Q8 | semidirect |
| 51. C2×C16×C53 | Q8 | semidirect |
| 146. C53 | #13291 | semidirect |
| 162. M32 | Dic106 | semidirect |
| 164. C2×C16 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285246 | 2 |
| #20274839 | 2 |
| #20272830 | 2 |
| #20272821 | 2 |
| #20272817 | 2 |
| #20272814 | 2 |
| C53×#2110 | 2 |
| #13291 | 53 |