Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1938 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1938 conjugacy classes of subgroups — too many to draw. Only its 291 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×#16811423 | C2 | semidirect |
| 2. C2×#16810591 | C2 | semidirect |
| 3. #20275820 | C2 | direct (N × H) |
| 4. C2×C53×#338 | C2 | semidirect |
| 8. #16811423 | C22 | semidirect |
| 14. #16810591 | C22 | semidirect |
| 17. C53×#338 | C22 | semidirect |
| 146. C2×#338 | D53 | semidirect |
| 149. C2×C53 | #2017 | semidirect |
| 164. #338 | C2×D53 | semidirect |
| 165. C53 | C2×#2017 | semidirect |
| 293. C2 | #20275820 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811423 | 2 |
| C2×#16810591 | 2 |
| #20275820 | 2 |
| C2×C53×#338 | 2 |
| C2×#2017 | 53 |