Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
294 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 71 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×#10622159 | C2 | semidirect |
| 3. #13066797 | C2 | semidirect |
| 4. C22⋊(C11⋊C32) | C2 | semidirect |
| 5. C22×C11×Q32 | C2 | semidirect |
| 27. C11×Q32 | D4 | semidirect |
| 57. C22×Q32 | D11 | semidirect |
| 93. C22×C11 | SD64 | semidirect |
| 113. Q32 | C22⋊D11 | semidirect |
| 147. C11 | #13662 | semidirect |
| 171. C22 | #10622159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622159 | 2 |
| #13070702 | 2 |
| #13066797 | 2 |
| C22⋊(C11⋊C32) | 2 |
| C22×C11×Q32 | 2 |
| #13662 | 11 |