Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276400 | C2 | semidirect |
| 3. #20272881 | C2 | semidirect |
| 4. C53×#2132 | C2 | semidirect |
| 14. #16810422 | C22 | semidirect |
| 18. C53×#356 | C22 | semidirect |
| 152. #2132 | D53 | semidirect |
| 172. #356 | C2×D53 | semidirect |
| 175. C53 | #13591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285168 | 2 |
| #20276400 | 2 |
| #20272881 | 2 |
| C53×#2132 | 2 |
| #13591 | 53 |