Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
774 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 255 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×#10587634 | C2 | semidirect |
| 3. #11762777 | C2 | semidirect |
| 4. #11762775 | C2 | semidirect |
| 5. #11762772 | C2 | semidirect |
| 6. C2×#10587491 | C2 | semidirect |
| 7. C2×C17×#131 | C2 | semidirect |
| 18. C2×M16×C17 | C22 | semidirect |
| 19. C22×C8×C17 | C22 | semidirect |
| 21. C2×#63223 | C22 | semidirect |
| 22. C22×#3622 | C22 | semidirect |
| 25. #10587491 | C22 | semidirect |
| 26. #10587491 | C22 | semidirect |
| 27. #10587491 | C22 | semidirect |
| 97. C2×D17 | #131 | semidirect |
| 105. C2×#131 | D17 | semidirect |
| 128. C2×M16 | C2×D17 | semidirect |
| 130. C22×C8 | C2×D17 | semidirect |
| 136. C17 | #2880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×D17 | 2 |
| C2×#10587634 | 2 |
| #11762777 | 2 |
| #11762775 | 2 |
| #11762772 | 2 |
| C2×#10587491 | 2 |
| C2×C17×#131 | 2 |
| #2880 | 17 |