Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #20290293 | C2 | semidirect |
| 4. #20290292 | C2 | semidirect |
| 5. #20289542 | C2 | semidirect |
| 6. #20289542 | C2 | semidirect |
| 25. #16810371 | C4 | semidirect |
| 26. #16810371 | C4 | semidirect |
| 27. #16810367 | C4 | semidirect |
| 28. C53×#331 | C4 | semidirect |
| 190. #331 | #6157 | semidirect |
| 191. C53 | #8935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291596 | 2 |
| #20290849 | 2 |
| #20290293 | 2 |
| #20290292 | 2 |
| #20289542 | 2 |
| #20273374 | 2 |
| #8935 | 53 |