Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
918 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 251 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. C22×#66891 | C2 | semidirect |
| 2. C2×#10622312 | C2 | semidirect |
| 3. #13070871 | C2 | direct (N × H) |
| 4. C2×C4×C11⋊C16 | C2 | semidirect |
| 16. C2×#66891 | C22 | semidirect |
| 19. #10622312 | C22 | semidirect |
| 20. C4×C11⋊C16 | C22 | semidirect |
| 45. C2×C11⋊C16 | D4 | semidirect |
| 76. C11⋊C16 | C2×D4 | semidirect |
| 90. C2×C4×C11 | SD32 | semidirect |
| 126. C4×C11 | C2×SD32 | semidirect |
| 157. C2×C11 | #2248 | semidirect |
| 189. C11 | C2×#2248 | semidirect |
| 203. C2×C4 | #66891 | semidirect |
| 220. C4 | C2×#66891 | semidirect |
| 224. C2 | #13070871 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66891 | 2 |
| C2×#10622312 | 2 |
| #13070871 | 2 |
| C2×C4×C11⋊C16 | 2 |
| C2×C11×#493 | 2 |
| C2×#2248 | 11 |