Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
806 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 195 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×C16×D11 | C2 | semidirect |
| 2. C2×#10622770 | C2 | semidirect |
| 3. #13070699 | C2 | direct (N × H) |
| 4. C2×#10622142 | C2 | semidirect |
| 5. C2×#10622200 | C2 | semidirect |
| 6. C22×C11×D16 | C2 | semidirect |
| 11. C2×C11×D16 | C22 | semidirect |
| 15. #10622770 | C22 | semidirect |
| 19. C2×C16×D11 | C22 | semidirect |
| 20. #10622200 | C22 | semidirect |
| 21. #10622142 | C22 | semidirect |
| 40. C2×C11×C16 | D4 | semidirect |
| 79. C11×C16 | C2×D4 | semidirect |
| 81. C22×D16 | D11 | semidirect |
| 94. C22×D11 | D16 | semidirect |
| 119. C2×D16 | C2×D11 | semidirect |
| 141. C2×D11 | C2×D16 | semidirect |
| 168. C2×C16 | C22⋊D11 | semidirect |
| 174. C2×C11 | #2215 | semidirect |
| 210. C16 | C2×C22⋊D11 | semidirect |
| 211. C11 | C2×#2215 | semidirect |
| 259. C2 | #13070699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D11 | 2 |
| C2×#10622770 | 2 |
| #13070699 | 2 |
| C2×#10622142 | 2 |
| C2×#10622200 | 2 |
| C22×C11×D16 | 2 |
| C2×#2215 | 11 |