Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
816 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20275529 | C2 | semidirect |
| 3. C2×#16810365 | C2 | semidirect |
| 4. C2×#16810362 | C2 | semidirect |
| 5. C53×#1992 | C2 | semidirect |
| 8. #16811371 | C4 | semidirect |
| 150. #1992 | D53 | semidirect |
| 176. C53 | #8508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811371 | 2 |
| #20275529 | 2 |
| C2×#16810365 | 2 |
| C2×#16810362 | 2 |
| C53×#1992 | 2 |
| #8508 | 53 |