Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2222 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2222 conjugacy classes of subgroups — too many to draw. Only its 667 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. #20280675 | C2 | direct (N × H) |
| 2. C2×#16810552 | C2 | semidirect |
| 3. C2×#16810547 | C2 | semidirect |
| 5. C2×#16810521 | C2 | semidirect |
| 6. C2×C53×#376 | C2 | semidirect |
| 12. #16810552 | C22 | semidirect |
| 13. #16810547 | C22 | semidirect |
| 15. #16810521 | C22 | semidirect |
| 18. C53×#376 | C22 | semidirect |
| 112. C2×#376 | D53 | semidirect |
| 113. C2×C53 | #2644 | semidirect |
| 128. #376 | C2×D53 | semidirect |
| 132. C53 | C2×#2644 | semidirect |
| 219. C2 | #20280675 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280675 | 2 |
| C2×#16810552 | 2 |
| C2×#16810547 | 2 |
| C2×#16810525 | 2 |
| C2×#16810521 | 2 |
| C2×C53×#376 | 2 |
| C2×#2644 | 53 |