Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20276192 | C2 | semidirect |
| 4. #20272538 | C2 | semidirect |
| 5. #20272537 | C2 | semidirect |
| 7. C53×#2083 | C2 | semidirect |
| 185. #2083 | D53 | semidirect |
| 216. C53 | #7793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20281675 | 2 |
| #20276244 | 2 |
| #20276192 | 2 |
| #20272538 | 2 |
| #20272537 | 2 |
| #20272535 | 2 |
| C53×#2083 | 2 |
| #7793 | 53 |