Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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×#10622809 | C2 | semidirect |
| 3. C2×#10622154 | C2 | semidirect |
| 4. #13069480 | C2 | semidirect |
| 5. #13066724 | C2 | semidirect |
| 6. #13066697 | C2 | semidirect |
| 7. C11×#2139 | C2 | semidirect |
| 17. #10622806 | C4 | semidirect |
| 90. C11×Q16 | C22⋊C4 | semidirect |
| 94. C11×D8 | C22⋊C4 | semidirect |
| 124. #2139 | D11 | semidirect |
| 274. Q16 | (C2×D11)⋊C4 | semidirect |
| 282. D8 | (C2×D11)⋊C4 | semidirect |
| 305. C11 | #13029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622806 | 2 |
| C2×#10622809 | 2 |
| C2×#10622154 | 2 |
| #13069480 | 2 |
| #13066724 | 2 |
| #13066697 | 2 |
| C11×#2139 | 2 |
| #13029 | 11 |