Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
178 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20272919 | C2 | semidirect |
| 4. #20272918 | C2 | semidirect |
| 5. C53×#1425 | C2 | semidirect |
| 58. #1425 | D53 | semidirect |
| 70. C53 | #13636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810456 | 2 |
| #368×D53 | 2 |
| #20272919 | 2 |
| #20272918 | 2 |
| C53×#1425 | 2 |
| #13636 | 53 |