Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
512 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 107 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×#10622508 | C2 | semidirect |
| 3. C2×#10622133 | C2 | semidirect |
| 4. #13070326 | C2 | semidirect |
| 5. #13069480 | C2 | semidirect |
| 6. #13066697 | C2 | semidirect |
| 7. C11×#1387 | C2 | semidirect |
| 20. #10622521 | C4 | semidirect |
| 108. Dic44 | C22⋊C4 | semidirect |
| 114. D88 | C22⋊C4 | semidirect |
| 126. #1387 | D11 | 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×#10622521 | 2 |
| C2×#10622508 | 2 |
| C2×#10622133 | 2 |
| #13070326 | 2 |
| #13069480 | 2 |
| #13066697 | 2 |
| C11×#1387 | 2 |
| #13029 | 11 |