Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. C2×#10622142 | C2 | semidirect |
| 3. #13066795 | C2 | direct (N × H) |
| 4. C22×C11×C32 | C2 | semidirect |
| 10. C2×D176 | C4 | semidirect |
| 13. C2×C11×C32 | C22 | semidirect |
| 15. #10622142 | C22 | semidirect |
| 31. D176 | C2×C4 | semidirect |
| 54. C22×C32 | D11 | semidirect |
| 82. C2×C32 | C2×D11 | semidirect |
| 114. C2×C11 | #1415 | semidirect |
| 138. C11 | C2×#1415 | semidirect |
| 169. C2 | #13066795 | 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×#10622142 | 2 |
| #13066795 | 2 |
| C22×C11×C32 | 2 |
| C2×#1415 | 11 |