Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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×#10622135 | C2 | semidirect |
| 3. #13070329 | C2 | semidirect |
| 4. C2×#10622200 | C2 | semidirect |
| 5. #13069402 | C2 | semidirect |
| 6. #13066706 | C2 | semidirect |
| 7. C2×C11×#361 | C2 | semidirect |
| 60. C11×#108 | D4 | semidirect |
| 125. C2×#361 | D11 | semidirect |
| 245. #108 | C22⋊D11 | semidirect |
| 312. C11 | #13411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079097 | 2 |
| C2×#10622135 | 2 |
| #13070329 | 2 |
| C2×#10622200 | 2 |
| #13069402 | 2 |
| #13066706 | 2 |
| C2×C11×#361 | 2 |
| #13411 | 11 |