Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1870 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 1870 conjugacy classes of subgroups — too many to draw. Only its 256 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×#16811643 | C2 | semidirect |
| 2. #20290242 | C2 | direct (N × H) |
| 3. C2×#16811481 | C2 | semidirect |
| 6. #16811643 | C22 | semidirect |
| 7. C2×#13133284 | C22 | semidirect |
| 10. #16811481 | C22 | semidirect |
| 23. #13133284 | C23 | semidirect |
| 174. C2×C53 | #1555 | semidirect |
| 194. C53 | C2×#1555 | semidirect |
| 344. C2 | #20290242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811643 | 2 |
| #20290242 | 2 |
| C2×#16811481 | 2 |
| C22×#13133213 | 2 |
| C2×#1555 | 53 |