Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20291210 | C2 | semidirect |
| 3. #20290229 | C2 | semidirect |
| 5. #20289569 | C2 | semidirect |
| 6. #20289538 | C2 | semidirect |
| 22. #16810995 | C4 | semidirect |
| 23. #16810974 | C4 | semidirect |
| 24. #16810973 | C4 | semidirect |
| 28. C53×#492 | C4 | semidirect |
| 103. C4×#6157 | SD16 | semidirect |
| 208. #492 | #6157 | semidirect |
| 226. C53 | #9301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291210 | 2 |
| #20290853 | 2 |
| #20290229 | 2 |
| #20290144 | 2 |
| #20289569 | 2 |
| #20289538 | 2 |
| #20285636 | 2 |
| #9301 | 53 |