Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 155 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×#16811055 | C2 | semidirect |
| 2. #20277022 | C2 | direct (N × H) |
| 3. C2×#16810463 | C2 | semidirect |
| 4. C2×#16810461 | C2 | semidirect |
| 5. C2×#16810460 | C2 | semidirect |
| 6. C2×#16810458 | C2 | semidirect |
| 7. C22×#13133123 | C2 | semidirect |
| 8. C2×C53×#508 | C2 | semidirect |
| 11. #16811055 | C22 | semidirect |
| 15. #16810463 | C22 | semidirect |
| 16. #16810461 | C22 | semidirect |
| 17. #16810460 | C22 | semidirect |
| 18. #16810458 | C22 | semidirect |
| 21. C2×#13133123 | C22 | semidirect |
| 24. C53×#508 | C22 | semidirect |
| 126. C2×#508 | D53 | semidirect |
| 135. C2×C53 | #2262 | semidirect |
| 143. #508 | C2×D53 | semidirect |
| 158. C53 | C2×#2262 | semidirect |
| 257. C2 | #20277022 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811055 | 2 |
| #20277022 | 2 |
| C2×#16810463 | 2 |
| C2×#16810461 | 2 |
| C2×#16810460 | 2 |
| C2×#16810458 | 2 |
| C22×#13133123 | 2 |
| C2×C53×#508 | 2 |
| C2×#2262 | 53 |