Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
446 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #20272609 | C2 | semidirect |
| 5. #20272607 | C2 | semidirect |
| 6. #20272579 | C2 | semidirect |
| 7. C53×#1288 | C2 | semidirect |
| 197. #1288 | D53 | semidirect |
| 224. C53 | #8773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277648 | 2 |
| C4×#13133133 | 2 |
| #20273055 | 2 |
| #20272609 | 2 |
| #20272607 | 2 |
| #20272579 | 2 |
| C53×#1288 | 2 |
| #8773 | 53 |