Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1050 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 219 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. #13071339 | C2 | semidirect |
| 3. #13069439 | C2 | semidirect |
| 4. #13068965 | C2 | semidirect |
| 5. #13068367 | C2 | semidirect |
| 6. C11×#1835 | C2 | semidirect |
| 16. #10622308 | C4 | semidirect |
| 31. C2×D88 | C2×C4 | semidirect |
| 34. #66927 | C2×C4 | semidirect |
| 35. C4×C8×C11 | C2×C4 | semidirect |
| 69. #1835 | D11 | semidirect |
| 135. C4×C8 | C4×D11 | semidirect |
| 166. C11 | #22276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622308 | 2 |
| #13071339 | 2 |
| #13069439 | 2 |
| #13068965 | 2 |
| #13068367 | 2 |
| C11×#1835 | 2 |
| #22276 | 11 |