Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#16810425 | C2 | semidirect |
| 3. C2×#16810425 | C2 | semidirect |
| 4. #20275448 | C2 | semidirect |
| 5. C53×#1374 | C2 | semidirect |
| 37. #13133151 | D4 | semidirect |
| 146. #1374 | D53 | semidirect |
| 167. C53 | #13407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811000 | 2 |
| C2×#16810425 | 2 |
| #20275448 | 2 |
| C53×#1374 | 2 |
| #13407 | 53 |