Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20275659 | C2 | semidirect |
| 5. #20273403 | C2 | semidirect |
| 6. #20272617 | C2 | semidirect |
| 7. C53×#1565 | C2 | semidirect |
| 92. M16×C53 | SD16 | semidirect |
| 189. #1565 | D53 | semidirect |
| 219. C53 | #10504 | semidirect |
| 287. M16 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285658 | 2 |
| #20275659 | 2 |
| #20275641 | 2 |
| #20275555 | 2 |
| #20273403 | 2 |
| #20272617 | 2 |
| C53×#1565 | 2 |
| #10504 | 53 |