Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1806 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 1806 conjugacy classes of subgroups — too many to draw. Only its 667 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. #13076885 | C2 | direct (N × H) |
| 33. C2×C42×C11 | Q8 | semidirect |
| 63. C42×C11 | C2×Q8 | semidirect |
| 132. C2×C42 | Dic22 | semidirect |
| 138. C2×C11 | #2843 | semidirect |
| 163. C42 | C2×Dic22 | semidirect |
| 164. C11 | C2×#2843 | semidirect |
| 195. C2 | #13076885 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13076885 | 2 |
| C2×#10622599 | 2 |
| C2×#10622597 | 2 |
| C2×#10622592 | 2 |
| C2×#10622550 | 2 |
| C2×C11×#384 | 2 |
| C2×#2843 | 11 |