Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
610 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 203 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. C2×#10622296 | C2 | semidirect |
| 3. #13070848 | C2 | direct (N × H) |
| 4. C2×#10622141 | C2 | semidirect |
| 6. C2×C4×C11×C16 | C2 | semidirect |
| 19. #10622296 | C22 | semidirect |
| 20. C4×C11×C16 | C22 | semidirect |
| 22. #10622141 | C22 | semidirect |
| 86. C2×C4×C16 | D11 | semidirect |
| 125. C4×C16 | C2×D11 | semidirect |
| 165. C2×C11 | #2242 | semidirect |
| 199. C11 | C2×#2242 | semidirect |
| 236. C2 | #13070848 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622296 | 2 |
| C2×#10622309 | 2 |
| #13070848 | 2 |
| C2×#10622141 | 2 |
| C2×#10622147 | 2 |
| C2×C4×C11×C16 | 2 |
| C2×#2242 | 11 |