Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #20273504 | C2 | semidirect |
| 4. #20273503 | C2 | semidirect |
| 6. #20272548 | C2 | semidirect |
| 7. C53×#1276 | C2 | semidirect |
| 22. #16810371 | C4 | semidirect |
| 23. #16810371 | C4 | semidirect |
| 24. #16810366 | C4 | semidirect |
| 25. #16810366 | C4 | semidirect |
| 164. #1276 | D53 | semidirect |
| 191. C53 | #8934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283781 | 2 |
| #20275543 | 2 |
| #20273504 | 2 |
| #20273503 | 2 |
| #20273375 | 2 |
| #20272548 | 2 |
| C53×#1276 | 2 |
| #8934 | 53 |