Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20290900 | C2 | semidirect |
| 3. C4×#13133271 | C2 | semidirect |
| 4. #20290273 | C2 | semidirect |
| 5. #20290065 | C2 | semidirect |
| 20. #16811021 | C4 | semidirect |
| 21. #16810973 | C4 | semidirect |
| 22. #16810969 | C4 | semidirect |
| 26. C53×#492 | C4 | semidirect |
| 140. C8×C53 | #104 | semidirect |
| 176. #492 | #6157 | semidirect |
| 192. C53 | #9851 | semidirect |
| 307. C8 | #13133281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290900 | 2 |
| #20290849 | 2 |
| C4×#13133271 | 2 |
| #20290273 | 2 |
| #20290065 | 2 |
| #20290061 | 2 |
| #20285272 | 2 |
| #9851 | 53 |