Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
562 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. C2×#16810372 | C2 | semidirect |
| 4. #20272550 | C2 | semidirect |
| 5. C2×C53×#500 | C2 | semidirect |
| 126. C2×#500 | D53 | semidirect |
| 150. C53 | #10278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810910 | 2 |
| #20275509 | 2 |
| C2×#16810372 | 2 |
| #20272550 | 2 |
| C2×C53×#500 | 2 |
| #10278 | 53 |