Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20276452 | C2 | semidirect |
| 3. #20274761 | C2 | semidirect |
| 4. #20272821 | C2 | semidirect |
| 5. C53×#3407 | C2 | semidirect |
| 8. #16810881 | C4 | semidirect |
| 9. #16810876 | C4 | semidirect |
| 50. M32×C53 | D4 | semidirect |
| 134. #3407 | D53 | semidirect |
| 159. C53 | #13077 | semidirect |
| 182. M32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284377 | 2 |
| #20276452 | 2 |
| #20274761 | 2 |
| #20272821 | 2 |
| C53×#3407 | 2 |
| #13077 | 53 |