Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1072 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20285175 | C2 | semidirect |
| 2. #20285108 | C2 | semidirect |
| 3. #20274021 | C2 | semidirect |
| 4. #20273307 | C2 | semidirect |
| 5. #20273307 | C2 | semidirect |
| 8. C2×#13133217 | C22 | semidirect |
| 9. #16811018 | C22 | semidirect |
| 12. #16810982 | C22 | semidirect |
| 16. C4×#11719917 | C22 | semidirect |
| 17. C4×#11719917 | C22 | semidirect |
| 18. #16810363 | C22 | semidirect |
| 19. #16810363 | C22 | semidirect |
| 199. C53 | #19074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285175 | 2 |
| #20285108 | 2 |
| #20274021 | 2 |
| #20273307 | 2 |
| C53×#3549 | 2 |
| #19074 | 53 |