Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
320 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20276512 | C2 | semidirect |
| 3. #335×D53 | C2 | semidirect |
| 4. #20272679 | C2 | semidirect |
| 5. #20272677 | C2 | semidirect |
| 6. #20272675 | C2 | semidirect |
| 7. C53×#1332 | C2 | semidirect |
| 153. #1332 | D53 | semidirect |
| 180. C53 | #11648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285288 | 2 |
| #20276512 | 2 |
| #335×D53 | 2 |
| #20272679 | 2 |
| #20272677 | 2 |
| #20272675 | 2 |
| C53×#1332 | 2 |
| #11648 | 53 |