Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 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 |
|---|---|---|
| 1. C2×#10622514 | C2 | semidirect |
| 2. #13078260 | C2 | semidirect |
| 3. #13070716 | C2 | semidirect |
| 4. #13070699 | C2 | semidirect |
| 5. #13070400 | C2 | semidirect |
| 6. #13070332 | C2 | semidirect |
| 7. C22×C11×D16 | C2 | semidirect |
| 17. #10622770 | C22 | semidirect |
| 21. C2×#66862 | C22 | semidirect |
| 22. C2×C16×D11 | C22 | semidirect |
| 23. #10622200 | C22 | semidirect |
| 24. #10622143 | C22 | semidirect |
| 25. #10622142 | C22 | semidirect |
| 45. C2×C11×C16 | D4 | semidirect |
| 88. C22×D16 | D11 | semidirect |
| 173. C2×C16 | C22⋊D11 | semidirect |
| 216. C11 | #33607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622514 | 2 |
| #13078260 | 2 |
| #13070716 | 2 |
| #13070699 | 2 |
| #13070400 | 2 |
| #13070332 | 2 |
| C22×C11×D16 | 2 |
| #33607 | 11 |