Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20274708 | C2 | semidirect |
| 5. #20273109 | C2 | semidirect |
| 6. #20272612 | C2 | semidirect |
| 7. C53×#1571 | C2 | semidirect |
| 170. #1571 | D53 | semidirect |
| 198. C53 | #10442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810824 | 2 |
| #20274708 | 2 |
| #20273384 | 2 |
| #20273382 | 2 |
| #20273109 | 2 |
| #20272612 | 2 |
| C53×#1571 | 2 |
| #10442 | 53 |