Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
598 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20284747 | C2 | semidirect |
| 3. #20278001 | C2 | semidirect |
| 4. #20275547 | C2 | semidirect |
| 5. #20273145 | C2 | semidirect |
| 6. #20273141 | C2 | semidirect |
| 7. C53×#1274 | C2 | semidirect |
| 217. #1274 | D53 | semidirect |
| 249. C53 | #10013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284747 | 2 |
| #20284716 | 2 |
| #20278001 | 2 |
| #20275547 | 2 |
| #20273145 | 2 |
| #20273141 | 2 |
| C53×#1274 | 2 |
| #10013 | 53 |