Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
960 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 247 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 |
|---|---|---|
| 1. C2×#16810671 | C2 | semidirect |
| 3. #20276117 | C2 | semidirect |
| 4. #20276114 | C2 | semidirect |
| 5. C2×C53×#338 | C2 | semidirect |
| 125. C2×#338 | D53 | semidirect |
| 142. C53 | #23622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810671 | 2 |
| C2×#16810605 | 2 |
| #20276117 | 2 |
| #20276114 | 2 |
| C2×C53×#338 | 2 |
| #23622 | 53 |