Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
502 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 155 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×#10622517 | C2 | semidirect |
| 2. C22×D176 | C2 | semidirect |
| 3. #13070931 | C2 | direct (N × H) |
| 4. C2×#10622087 | C2 | semidirect |
| 5. C2×D352 | C2 | semidirect |
| 6. C2×C11×M64 | C2 | semidirect |
| 10. C2×Dic88 | C22 | semidirect |
| 12. #10622517 | C22 | semidirect |
| 17. C2×D176 | C22 | semidirect |
| 18. C2×D176 | C22 | semidirect |
| 19. C11×M64 | C22 | semidirect |
| 20. C2×C11×C32 | C22 | semidirect |
| 21. #10622087 | C22 | semidirect |
| 22. D352 | C22 | semidirect |
| 40. Dic88 | C23 | semidirect |
| 46. D176 | C23 | semidirect |
| 47. C11×C32 | C23 | semidirect |
| 81. C2×M64 | D11 | semidirect |
| 118. M64 | C2×D11 | semidirect |
| 119. C2×C32 | C2×D11 | semidirect |
| 156. C32 | C22×D11 | semidirect |
| 158. C2×C11 | #2263 | semidirect |
| 189. C11 | C2×#2263 | semidirect |
| 227. C2 | #13070931 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622517 | 2 |
| C22×D176 | 2 |
| #13070931 | 2 |
| C2×#10622087 | 2 |
| C2×D352 | 2 |
| C2×C11×M64 | 2 |
| C2×#2263 | 11 |