Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1164 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 271 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. #13069792 | C2 | semidirect |
| 3. #13068348 | C2 | semidirect |
| 4. C11×#3458 | C2 | semidirect |
| 21. C22×D44 | Q8 | semidirect |
| 22. C22×C4×D11 | Q8 | semidirect |
| 23. C22×Dic22 | Q8 | semidirect |
| 83. #3458 | D11 | semidirect |
| 214. C11 | #23474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622619 | 2 |
| #13069792 | 2 |
| #13068348 | 2 |
| C11×#3458 | 2 |
| #23474 | 11 |