Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
746 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 746 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20273416 | C2 | semidirect |
| 4. #20273415 | C2 | semidirect |
| 5. #20273329 | C2 | semidirect |
| 7. C53×#1531 | C2 | semidirect |
| 215. #1531 | D53 | semidirect |
| 247. C53 | #8457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288516 | 2 |
| #20275513 | 2 |
| #20273416 | 2 |
| #20273415 | 2 |
| #20273329 | 2 |
| #20273055 | 2 |
| C53×#1531 | 2 |
| #8457 | 53 |