Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
890 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20276344 | C2 | semidirect |
| 3. C2×#16810406 | C2 | semidirect |
| 4. #20276336 | C2 | semidirect |
| 5. C53×#2113 | C2 | semidirect |
| 14. C2×#13133157 | C22 | semidirect |
| 19. C2×M32×C53 | C22 | semidirect |
| 20. C22×C16×C53 | C22 | semidirect |
| 164. #2113 | D53 | semidirect |
| 180. C2×M32 | C2×D53 | semidirect |
| 181. C22×C16 | C2×D53 | semidirect |
| 186. C53 | #12685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289426 | 2 |
| #20276344 | 2 |
| C2×#16810406 | 2 |
| #20276336 | 2 |
| C53×#2113 | 2 |
| #12685 | 53 |