Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
520 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20284366 | C2 | semidirect |
| 3. C2×#16810439 | C2 | semidirect |
| 4. #20276451 | C2 | semidirect |
| 5. #20276344 | C2 | semidirect |
| 6. #20272830 | C2 | semidirect |
| 7. C2×C53×#510 | C2 | semidirect |
| 200. C2×#510 | D53 | semidirect |
| 236. C53 | #13311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284431 | 2 |
| #20284366 | 2 |
| C2×#16810439 | 2 |
| #20276451 | 2 |
| #20276344 | 2 |
| #20272830 | 2 |
| C2×C53×#510 | 2 |
| #13311 | 53 |