Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
676 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 3. #20289535 | C2 | semidirect |
| 56. C2×Q8×C53 | M16 | semidirect |
| 189. C53 | #7609 | semidirect |
| 226. C2×Q8 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290606 | 2 |
| #20290378 | 2 |
| #20289535 | 2 |
| C2×#16810530 | 2 |
| #7609 | 53 |