Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1180 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1180 conjugacy classes of subgroups — too many to draw. Only its 191 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×#16810997 | C2 | semidirect |
| 3. #20280482 | C2 | semidirect |
| 4. #20275717 | C2 | semidirect |
| 5. #20275681 | C2 | semidirect |
| 6. #20275539 | C2 | semidirect |
| 7. #20275046 | C2 | semidirect |
| 8. #20274484 | C2 | semidirect |
| 9. C2×C53×#491 | C2 | semidirect |
| 192. C2×#491 | D53 | semidirect |
| 230. C53 | #25606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811229 | 2 |
| C2×#16810997 | 2 |
| #20280482 | 2 |
| #20275717 | 2 |
| #20275681 | 2 |
| #20275539 | 2 |
| #20275046 | 2 |
| #20274484 | 2 |
| C2×C53×#491 | 2 |
| #25606 | 53 |