Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
914 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 152 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. #20289618 | C2 | semidirect |
| 7. #16811593 | C4 | semidirect |
| 10. C2×C22⋊#88324 | C4 | semidirect |
| 191. C53 | #8112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811593 | 2 |
| #20289618 | 2 |
| #20277093 | 2 |
| #8112 | 53 |