Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
468 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 468 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. #20290622 | C2 | semidirect |
| 3. #20290609 | C2 | semidirect |
| 5. #20289598 | C2 | semidirect |
| 6. #20289556 | C2 | semidirect |
| 27. #16810958 | C4 | semidirect |
| 28. #16810954 | C4 | semidirect |
| 30. #16810934 | C4 | semidirect |
| 34. C53×#481 | C4 | semidirect |
| 243. #481 | #6157 | semidirect |
| 264. C53 | #9038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291582 | 2 |
| #20290622 | 2 |
| #20290609 | 2 |
| #20290091 | 2 |
| #20289598 | 2 |
| #20289556 | 2 |
| #20284625 | 2 |
| #9038 | 53 |