Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 470 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. #20275660 | C2 | semidirect |
| 5. #20273465 | C2 | semidirect |
| 6. #20272616 | C2 | semidirect |
| 7. C53×#1550 | C2 | semidirect |
| 115. #11719917 | SD16 | semidirect |
| 190. #1550 | D53 | semidirect |
| 219. C53 | #10504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285653 | 2 |
| #20275660 | 2 |
| #20275641 | 2 |
| #20275554 | 2 |
| #20273465 | 2 |
| #20272616 | 2 |
| C53×#1550 | 2 |
| #10504 | 53 |