Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 72 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. #20290125 | C2 | semidirect |
| 4. #20289995 | C2 | semidirect |
| 5. #20289619 | C2 | semidirect |
| 6. #20289586 | C2 | semidirect |
| 27. #16810956 | C4 | semidirect |
| 28. #16810942 | C4 | semidirect |
| 32. #16810762 | C4 | semidirect |
| 34. C53×#451 | C4 | semidirect |
| 232. #451 | #6157 | semidirect |
| 251. C53 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291594 | 2 |
| #20290142 | 2 |
| #20290125 | 2 |
| #20289995 | 2 |
| #20289619 | 2 |
| #20289586 | 2 |
| #20285548 | 2 |
| #9331 | 53 |