Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
676 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #20280088 | C2 | semidirect |
| 4. C2×#16810353 | C2 | semidirect |
| 5. C53×#1296 | C2 | semidirect |
| 70. C2×Dic106 | SD16 | semidirect |
| 151. #1296 | D53 | semidirect |
| 172. C53 | #10230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810824 | 2 |
| #20280088 | 2 |
| #20275520 | 2 |
| C2×#16810353 | 2 |
| C53×#1296 | 2 |
| #10230 | 53 |