Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1170 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 230 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. #20291618 | C2 | semidirect |
| 2. #20289985 | C2 | semidirect |
| 3. #20289974 | C2 | semidirect |
| 4. #20289954 | C2 | semidirect |
| 183. C53 | #17425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291618 | 2 |
| #20289985 | 2 |
| #20289974 | 2 |
| #20289954 | 2 |
| C2×#16811280 | 2 |
| #17425 | 53 |