Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3774 conjugacy classes of subgroups; only the 1579 normal subgroups are shown.
This group has 3774 conjugacy classes of subgroups — too many to draw. Only its 1579 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. #13077014 | C2 | direct (N × H) |
| 19. C2×C42×C11 | Q8 | semidirect |
| 37. C42×C11 | C2×Q8 | semidirect |
| 47. C2×C4×C11 | C4⋊Q8 | semidirect |
| 67. C4×C11 | C2×C4⋊Q8 | semidirect |
| 77. C2×C42 | Dic22 | semidirect |
| 81. C2×C11 | #2868 | semidirect |
| 95. C42 | C2×Dic22 | semidirect |
| 97. C11 | C2×#2868 | semidirect |
| 104. C2×C4 | #66922 | semidirect |
| 114. C4 | C2×#66922 | semidirect |
| 116. C2 | #13077014 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66922 | 2 |
| #13077014 | 2 |
| C2×#10622548 | 2 |
| C2×C43×C11 | 2 |
| C2×#2868 | 11 |