Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
510 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 88 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. #20291527 | C2 | semidirect |
| 2. #20290587 | C2 | semidirect |
| 3. #20290095 | C2 | semidirect |
| 4. #20290061 | C2 | semidirect |
| 5. #20289607 | C2 | semidirect |
| 6. #20289549 | C2 | semidirect |
| 27. #16810834 | C4 | semidirect |
| 28. #16810828 | C4 | semidirect |
| 29. #16810820 | C4 | semidirect |
| 32. C53×#459 | C4 | semidirect |
| 245. #459 | #6157 | semidirect |
| 262. C53 | #9210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291527 | 2 |
| #20290587 | 2 |
| #20290095 | 2 |
| #20290061 | 2 |
| #20289607 | 2 |
| #20289549 | 2 |
| #20284163 | 2 |
| #9210 | 53 |