Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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×#10622719 | C2 | semidirect |
| 3. #13070825 | C2 | semidirect |
| 4. #13070808 | C2 | semidirect |
| 5. #13070404 | C2 | semidirect |
| 6. #13070329 | C2 | semidirect |
| 7. C11×#2112 | C2 | semidirect |
| 23. #10622147 | C22 | semidirect |
| 24. #10622143 | C22 | semidirect |
| 25. #10622142 | C22 | semidirect |
| 26. #10622141 | C22 | semidirect |
| 101. #2112 | D11 | semidirect |
| 237. C11 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13078197 | 2 |
| C2×#10622719 | 2 |
| #13070825 | 2 |
| #13070808 | 2 |
| #13070404 | 2 |
| #13070329 | 2 |
| C11×#2112 | 2 |
| #33647 | 11 |