Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
918 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 267 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×#66864 | C2 | semidirect |
| 2. C2×#10622312 | C2 | semidirect |
| 4. #13070872 | C2 | direct (N × H) |
| 5. C2×C4×C11×C16 | C2 | semidirect |
| 15. C2×#66864 | C22 | semidirect |
| 17. #10622312 | C22 | semidirect |
| 20. C4×C11×C16 | C22 | semidirect |
| 42. C2×C11×C16 | D4 | semidirect |
| 76. C11×C16 | C2×D4 | semidirect |
| 81. C2×C4×C16 | D11 | semidirect |
| 86. C2×C4×C11 | SD32 | semidirect |
| 118. C4×C16 | C2×D11 | semidirect |
| 126. C4×C11 | C2×SD32 | semidirect |
| 152. C2×C16 | D44 | semidirect |
| 156. C2×C11 | #2248 | semidirect |
| 188. C16 | C2×D44 | semidirect |
| 189. C11 | C2×#2248 | semidirect |
| 203. C2×C4 | #66864 | semidirect |
| 220. C4 | C2×#66864 | semidirect |
| 224. C2 | #13070872 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66864 | 2 |
| C2×#10622312 | 2 |
| C2×#10622308 | 2 |
| #13070872 | 2 |
| C2×C4×C11×C16 | 2 |
| C2×#2248 | 11 |