Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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. #20291084 | C2 | semidirect |
| 2. #20289719 | C2 | semidirect |
| 3. #20289718 | C2 | semidirect |
| 7. #16811515 | C22 | semidirect |
| 123. C53 | #11915 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291084 | 2 |
| #20289719 | 2 |
| #20289718 | 2 |
| #20285091 | 2 |
| #11915 | 53 |