Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
848 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#16810421 | C2 | semidirect |
| 3. C2×#16810420 | C2 | semidirect |
| 4. C2×#16810419 | C2 | semidirect |
| 5. #20275118 | C2 | semidirect |
| 6. #20275108 | C2 | semidirect |
| 7. C53×#1888 | C2 | semidirect |
| 11. #16811335 | C4 | semidirect |
| 250. #1888 | D53 | semidirect |
| 284. C53 | #12776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811335 | 2 |
| C2×#16810421 | 2 |
| C2×#16810420 | 2 |
| C2×#16810419 | 2 |
| #20275118 | 2 |
| #20275108 | 2 |
| C53×#1888 | 2 |
| #12776 | 53 |