Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
248 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20272544 | C2 | semidirect |
| 3. C53×#1274 | C2 | semidirect |
| 13. #13133217 | C8 | semidirect |
| 14. #13133214 | C8 | semidirect |
| 112. #1274 | D53 | semidirect |
| 125. C53 | #7115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275547 | 2 |
| #20272544 | 2 |
| C53×#1274 | 2 |
| #7115 | 53 |