Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
194 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20276992 | C2 | semidirect |
| 3. #20272894 | C2 | semidirect |
| 4. #20272893 | C2 | semidirect |
| 5. #20272892 | C2 | semidirect |
| 6. #20272848 | C2 | semidirect |
| 7. C53×#1415 | C2 | semidirect |
| 91. #1415 | D53 | semidirect |
| 109. C53 | #13723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276992 | 2 |
| #20276963 | 2 |
| #20272894 | 2 |
| #20272893 | 2 |
| #20272892 | 2 |
| #20272848 | 2 |
| C53×#1415 | 2 |
| #13723 | 53 |