Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1022 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 219 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×D176 | C2 | semidirect |
| 2. C22×#66890 | C2 | semidirect |
| 3. C2×#10622764 | C2 | semidirect |
| 4. #13070864 | C2 | direct (N × H) |
| 5. C2×C16×Dic11 | C2 | semidirect |
| 6. C22×C11×D16 | C2 | semidirect |
| 12. C2×C11×D16 | C22 | semidirect |
| 15. #10622764 | C22 | semidirect |
| 17. C2×#66890 | C22 | semidirect |
| 21. C2×D176 | C22 | semidirect |
| 22. C16×Dic11 | C22 | semidirect |
| 42. C2×C11×C16 | D4 | semidirect |
| 47. C2×C11⋊C16 | D4 | semidirect |
| 80. C11×C16 | C2×D4 | semidirect |
| 81. C11⋊C16 | C2×D4 | semidirect |
| 84. C22×D16 | D11 | semidirect |
| 103. C2×Dic11 | D16 | semidirect |
| 121. C2×D16 | C2×D11 | semidirect |
| 140. Dic11 | C2×D16 | semidirect |
| 164. C2×C16 | C22⋊D11 | semidirect |
| 169. C2×C11 | #2246 | semidirect |
| 203. C16 | C2×C22⋊D11 | semidirect |
| 204. C11 | C2×#2246 | semidirect |
| 244. C2 | #13070864 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D176 | 2 |
| C22×#66890 | 2 |
| C2×#10622764 | 2 |
| #13070864 | 2 |
| C2×C16×Dic11 | 2 |
| C22×C11×D16 | 2 |
| C2×#2246 | 11 |