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. C22×D176 | C2 | semidirect |
| 2. C2×#10622514 | C2 | semidirect |
| 3. #13078265 | C2 | semidirect |
| 4. #13070720 | C2 | semidirect |
| 5. #13070703 | C2 | semidirect |
| 6. #13070331 | C2 | semidirect |
| 7. C11×#2158 | C2 | semidirect |
| 19. C2×#66862 | C22 | semidirect |
| 20. C2×C16×D11 | C22 | semidirect |
| 21. #10622496 | C22 | semidirect |
| 23. C11×#367 | C22 | semidirect |
| 24. C11×#366 | C22 | semidirect |
| 25. #10622129 | C22 | semidirect |
| 43. C2×C11×C16 | D4 | semidirect |
| 93. #2158 | D11 | semidirect |
| 134. #367 | C2×D11 | semidirect |
| 135. #366 | C2×D11 | semidirect |
| 173. C2×C16 | D44 | semidirect |
| 216. C11 | #33607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D176 | 2 |
| C2×#10622514 | 2 |
| #13078265 | 2 |
| #13070720 | 2 |
| #13070703 | 2 |
| #13070331 | 2 |
| C11×#2158 | 2 |
| #33607 | 11 |