Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
936 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. C2×#16811373 | C2 | semidirect |
| 2. #20285901 | C2 | semidirect |
| 3. #20274024 | C2 | semidirect |
| 4. #20274011 | C2 | semidirect |
| 5. #20273339 | C2 | semidirect |
| 6. #20273316 | C2 | semidirect |
| 16. #16811029 | C22 | semidirect |
| 17. #16810987 | C22 | semidirect |
| 22. #16810364 | C22 | semidirect |
| 218. C53 | #18994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811373 | 2 |
| #20285901 | 2 |
| #20274024 | 2 |
| #20274011 | 2 |
| #20273339 | 2 |
| #20273316 | 2 |
| C53×#3153 | 2 |
| #18994 | 53 |