Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10587618 | C2 | semidirect |
| 2. C2×#10587590 | C2 | semidirect |
| 3. #11763376 | C2 | semidirect |
| 4. #11763197 | C2 | semidirect |
| 5. #11763192 | C2 | semidirect |
| 6. #11763184 | C2 | semidirect |
| 7. #11762764 | C2 | semidirect |
| 8. C22×D8×C17 | C2 | semidirect |
| 16. #10587626 | C22 | semidirect |
| 18. #10587622 | C22 | semidirect |
| 19. C2×#63229 | C22 | semidirect |
| 21. C2×#63228 | C22 | semidirect |
| 24. C2×Dic68 | C22 | semidirect |
| 26. C2×D136 | C22 | semidirect |
| 27. C2×#63219 | C22 | semidirect |
| 28. #10587486 | C22 | semidirect |
| 29. C8×Dic17 | C22 | semidirect |
| 45. C2×C8×C17 | D4 | semidirect |
| 54. #63223 | D4 | semidirect |
| 99. C22×D8 | D17 | semidirect |
| 131. C17 | #3155 | semidirect |
| 154. C2×C8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587618 | 2 |
| C2×#10587590 | 2 |
| #11763376 | 2 |
| #11763197 | 2 |
| #11763192 | 2 |
| #11763184 | 2 |
| #11762764 | 2 |
| C22×D8×C17 | 2 |
| #3155 | 17 |