Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20277027 | C2 | semidirect |
| 2. C2×#16810458 | C2 | semidirect |
| 3. #20276835 | C2 | semidirect |
| 4. #20272905 | C2 | semidirect |
| 5. #20272899 | C2 | semidirect |
| 6. #20272857 | C2 | semidirect |
| 7. C53×#3415 | C2 | semidirect |
| 8. C2×D848 | C22 | semidirect |
| 13. #16810457 | C22 | semidirect |
| 14. C2×#13133123 | C22 | semidirect |
| 15. #16810453 | C22 | semidirect |
| 116. #3415 | D53 | semidirect |
| 146. C53 | #13669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277027 | 2 |
| C2×#16810458 | 2 |
| #20276835 | 2 |
| #20272905 | 2 |
| #20272899 | 2 |
| #20272857 | 2 |
| C53×#3415 | 2 |
| #13669 | 53 |