Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20275703 | C2 | semidirect |
| 3. #20275638 | C2 | semidirect |
| 5. #20273468 | C2 | semidirect |
| 7. C53×#1303 | C2 | semidirect |
| 112. #11719917 | SD16 | semidirect |
| 187. #1303 | D53 | semidirect |
| 215. C53 | #10501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285642 | 2 |
| #20275703 | 2 |
| #20275638 | 2 |
| #20275633 | 2 |
| #20273468 | 2 |
| #20273393 | 2 |
| C53×#1303 | 2 |
| #10501 | 53 |