Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20276274 | C2 | semidirect |
| 3. #20276188 | C2 | semidirect |
| 5. #20272537 | C2 | semidirect |
| 6. #20272537 | C2 | semidirect |
| 214. C53 | #7788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20281645 | 2 |
| #20276274 | 2 |
| #20276188 | 2 |
| #20276118 | 2 |
| #20272537 | 2 |
| C53×#1270 | 2 |
| #7788 | 53 |