Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20274852 | C2 | semidirect |
| 3. #20273167 | C2 | semidirect |
| 4. #20273166 | C2 | semidirect |
| 5. #20273165 | C2 | semidirect |
| 6. C2×#16810344 | C2 | semidirect |
| 7. C53×#1492 | C2 | semidirect |
| 173. #1492 | D53 | semidirect |
| 200. C53 | #9860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285141 | 2 |
| #20274852 | 2 |
| #20273167 | 2 |
| #20273166 | 2 |
| #20273165 | 2 |
| C2×#16810344 | 2 |
| C53×#1492 | 2 |
| #9860 | 53 |