Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
316 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #20276320 | C2 | semidirect |
| 5. #20272828 | C2 | semidirect |
| 6. #20272826 | C2 | semidirect |
| 7. C53×#1953 | C2 | semidirect |
| 15. #16810435 | C4 | semidirect |
| 129. #1953 | D53 | semidirect |
| 151. C53 | #13158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810435 | 2 |
| #20276320 | 2 |
| #20275625 | 2 |
| #20272828 | 2 |
| #20272826 | 2 |
| C53×#1953 | 2 |
| #13158 | 53 |