Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
748 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20275547 | C2 | semidirect |
| 3. #20273446 | C2 | semidirect |
| 4. #20273437 | C2 | semidirect |
| 5. #20273349 | C2 | semidirect |
| 6. #20273226 | C2 | semidirect |
| 7. C53×#1505 | C2 | semidirect |
| 10. #16811330 | C4 | semidirect |
| 11. #16811294 | C4 | semidirect |
| 222. #1505 | D53 | semidirect |
| 254. C53 | #8493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289113 | 2 |
| #20275547 | 2 |
| #20273446 | 2 |
| #20273437 | 2 |
| #20273349 | 2 |
| #20273226 | 2 |
| C53×#1505 | 2 |
| #8493 | 53 |