Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 26. #16811033 | C4 | semidirect |
| 27. #16811032 | C4 | semidirect |
| 28. #16811029 | C4 | semidirect |
| 34. C53×#501 | C4 | semidirect |
| 215. #501 | #6157 | semidirect |
| 237. C53 | #9440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291250 | 2 |
| #20290198 | 2 |
| #20290109 | 2 |
| #20290107 | 2 |
| #20289604 | 2 |
| #20285266 | 2 |
| #9440 | 53 |