Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20275645 | C2 | semidirect |
| 3. #20273498 | C2 | semidirect |
| 4. #20273210 | C2 | semidirect |
| 5. #20273068 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 7. C53×#1551 | C2 | semidirect |
| 190. #1551 | D53 | semidirect |
| 222. C53 | #10508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285698 | 2 |
| #20275645 | 2 |
| #20273498 | 2 |
| #20273210 | 2 |
| #20273068 | 2 |
| #20272570 | 2 |
| C53×#1551 | 2 |
| #10508 | 53 |