Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
256 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 20. #10622131 | C4 | semidirect |
| 182. C11 | #13175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070410 | 2 |
| C2×#10622132 | 2 |
| #13070221 | 2 |
| #13069396 | 2 |
| #13066719 | 2 |
| #13066716 | 2 |
| C11×#1953 | 2 |
| #13175 | 11 |