Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
610 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 203 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×#16811025 | C2 | semidirect |
| 3. #20276947 | C2 | direct (N × H) |
| 4. C2×#16810428 | C2 | semidirect |
| 6. C2×C4×C16×C53 | C2 | semidirect |
| 13. #16811025 | C22 | semidirect |
| 18. #16810428 | C22 | semidirect |
| 22. C4×C16×C53 | C22 | semidirect |
| 121. C2×C4×C16 | D53 | semidirect |
| 122. C2×C53 | #2242 | semidirect |
| 141. C4×C16 | C2×D53 | semidirect |
| 142. C53 | C2×#2242 | semidirect |
| 236. C2 | #20276947 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811025 | 2 |
| C2×#16811007 | 2 |
| #20276947 | 2 |
| C2×#16810428 | 2 |
| C2×#16810425 | 2 |
| C2×C4×C16×C53 | 2 |
| C2×#2242 | 53 |