Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
798 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 227 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. #20285274 | C2 | semidirect |
| 2. #20285229 | C2 | semidirect |
| 4. #20274348 | C2 | semidirect |
| 5. #20274343 | C2 | semidirect |
| 6. #20274337 | C2 | semidirect |
| 7. C2×C53×#322 | C2 | semidirect |
| 68. C2×C8×C53 | SD16 | semidirect |
| 123. C2×#322 | D53 | semidirect |
| 149. C53 | #19608 | semidirect |
| 193. C2×C8 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285274 | 2 |
| #20285229 | 2 |
| #20285143 | 2 |
| #20274348 | 2 |
| #20274343 | 2 |
| #20274337 | 2 |
| C2×C53×#322 | 2 |
| #19608 | 53 |