Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 27. #16810365 | C4 | semidirect |
| 28. #16810364 | C4 | semidirect |
| 29. #16810364 | C4 | semidirect |
| 30. C53×#330 | C4 | semidirect |
| 189. #330 | #6157 | semidirect |
| 190. C53 | #8919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291628 | 2 |
| #20290902 | 2 |
| #20290281 | 2 |
| #20290280 | 2 |
| #20289604 | 2 |
| #20273308 | 2 |
| #8919 | 53 |