Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 92 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. #20290428 | C2 | semidirect |
| 4. #20290274 | C2 | semidirect |
| 5. #20290065 | C2 | semidirect |
| 20. #16811021 | C4 | semidirect |
| 21. #16810973 | C4 | semidirect |
| 22. #16810969 | C4 | semidirect |
| 26. C53×#492 | C4 | semidirect |
| 175. #492 | #6157 | semidirect |
| 191. C53 | #9854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290900 | 2 |
| #20290849 | 2 |
| #20290428 | 2 |
| #20290274 | 2 |
| #20290065 | 2 |
| #20290061 | 2 |
| #20285272 | 2 |
| #9854 | 53 |