Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
798 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 211 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 |
|---|---|---|
| 1. #20285275 | C2 | semidirect |
| 3. #20274349 | C2 | semidirect |
| 4. #20274344 | C2 | semidirect |
| 5. #20274338 | C2 | semidirect |
| 6. C2×#16810344 | C2 | semidirect |
| 7. C53×#3160 | C2 | semidirect |
| 67. C2×C8×C53 | SD16 | semidirect |
| 118. #3160 | D53 | semidirect |
| 149. C53 | #19608 | semidirect |
| 194. C2×C8 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285275 | 2 |
| #20285143 | 2 |
| #20274349 | 2 |
| #20274344 | 2 |
| #20274338 | 2 |
| C2×#16810344 | 2 |
| C53×#3160 | 2 |
| #19608 | 53 |