Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
522 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 2. #20290454 | C2 | semidirect |
| 3. #20290449 | C2 | semidirect |
| 5. #20289598 | C2 | semidirect |
| 6. #20289596 | C2 | semidirect |
| 8. C2×#13133304 | C4 | semidirect |
| 14. #16811630 | C4 | semidirect |
| 15. #16811597 | C4 | semidirect |
| 18. #16811588 | C4 | semidirect |
| 24. #16811476 | C4 | semidirect |
| 25. #16811474 | C4 | semidirect |
| 29. #16810361 | C4 | semidirect |
| 30. #16810359 | C4 | semidirect |
| 31. #16810357 | C4 | semidirect |
| 32. C53×#327 | C4 | semidirect |
| 257. #327 | #6157 | semidirect |
| 258. C53 | #8240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291429 | 2 |
| #20290454 | 2 |
| #20290449 | 2 |
| #20290091 | 2 |
| #20289598 | 2 |
| #20289596 | 2 |
| #20273203 | 2 |
| #8240 | 53 |