Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1022 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1022 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×D176 | C2 | semidirect |
| 2. C2×#10622308 | C2 | semidirect |
| 3. #13070866 | C2 | direct (N × H) |
| 4. C2×C4×C11×C16 | C2 | semidirect |
| 11. C2×D176 | C22 | semidirect |
| 13. #10622308 | C22 | semidirect |
| 14. C4×C11×C16 | C22 | semidirect |
| 27. C2×C11×C16 | D4 | semidirect |
| 52. C11×C16 | C2×D4 | semidirect |
| 56. C2×C4×C16 | D11 | semidirect |
| 61. C2×C4×C11 | D16 | semidirect |
| 83. C4×C16 | C2×D11 | semidirect |
| 91. C4×C11 | C2×D16 | semidirect |
| 107. C2×C16 | D44 | semidirect |
| 111. C2×C11 | #2246 | semidirect |
| 134. C16 | C2×D44 | semidirect |
| 135. C11 | C2×#2246 | semidirect |
| 144. C2×C4 | D176 | semidirect |
| 160. C4 | C2×D176 | semidirect |
| 164. C2 | #13070866 | 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 |
| C2×#10622308 | 2 |
| #13070866 | 2 |
| C2×C4×C11×C16 | 2 |
| C2×#2246 | 11 |