Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
442 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 79 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. #13070225 | C2 | semidirect |
| 3. #13068653 | C2 | semidirect |
| 4. #13066632 | C2 | semidirect |
| 5. #13066631 | C2 | semidirect |
| 6. #13066630 | C2 | semidirect |
| 7. C11×#1349 | C2 | semidirect |
| 22. C11×C22⋊C16 | C22 | semidirect |
| 23. C11×#341 | C22 | semidirect |
| 24. #10622190 | C22 | semidirect |
| 25. C22⋊(C11⋊C16) | C22 | semidirect |
| 120. #1349 | D11 | semidirect |
| 179. C22⋊C16 | C2×D11 | semidirect |
| 181. #341 | C2×D11 | semidirect |
| 301. C11 | #11895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D11×#466 | 2 |
| #13070225 | 2 |
| #13068653 | 2 |
| #13066632 | 2 |
| #13066631 | 2 |
| #13066630 | 2 |
| C11×#1349 | 2 |
| #11895 | 11 |