Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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×#10622160 | C2 | semidirect |
| 3. C2×#10622159 | C2 | semidirect |
| 4. #13066796 | C2 | semidirect |
| 5. #13066793 | C2 | semidirect |
| 6. C22⋊(C11⋊C32) | C2 | semidirect |
| 7. C11×#2216 | C2 | semidirect |
| 76. #2216 | D11 | semidirect |
| 182. C11 | #13666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622517 | 2 |
| C2×#10622160 | 2 |
| C2×#10622159 | 2 |
| #13066796 | 2 |
| #13066793 | 2 |
| C22⋊(C11⋊C32) | 2 |
| C11×#2216 | 2 |
| #13666 | 11 |