Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20290890 | C2 | semidirect |
| 3. #20290109 | C2 | semidirect |
| 5. #20289602 | C2 | semidirect |
| 6. #20289567 | C2 | semidirect |
| 25. #16810900 | C4 | semidirect |
| 26. #16810829 | C4 | semidirect |
| 27. #16810828 | C4 | semidirect |
| 32. C53×#474 | C4 | semidirect |
| 230. #474 | #6157 | semidirect |
| 251. C53 | #9327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291198 | 2 |
| #20290890 | 2 |
| #20290109 | 2 |
| #20290055 | 2 |
| #20289602 | 2 |
| #20289567 | 2 |
| #20284816 | 2 |
| #9327 | 53 |