Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
794 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 2. #20289813 | C2 | semidirect |
| 3. #20289812 | C2 | semidirect |
| 7. #16811610 | C4 | semidirect |
| 25. #13133278 | C2×C4 | semidirect |
| 199. C53 | #12587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811610 | 2 |
| #20289813 | 2 |
| #20289812 | 2 |
| #20277305 | 2 |
| #12587 | 53 |