Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#10587694 | C2 | semidirect |
| 2. C2×#10587594 | C2 | semidirect |
| 3. C22×#63230 | C2 | semidirect |
| 4. #11763378 | C2 | semidirect |
| 5. #11762957 | C2 | semidirect |
| 6. #11762949 | C2 | semidirect |
| 7. #11762803 | C2 | semidirect |
| 8. #11762777 | C2 | semidirect |
| 9. C17×#419 | C2 | semidirect |
| 14. C2×#63256 | C22 | semidirect |
| 16. C2×Q8×D17 | C22 | semidirect |
| 33. C17×#103 | C22 | semidirect |
| 34. #10587491 | C22 | semidirect |
| 35. #10587481 | C22 | semidirect |
| 36. #10587480 | C22 | semidirect |
| 40. C2×Q8×C17 | D4 | semidirect |
| 56. #63252 | D4 | semidirect |
| 146. #419 | D17 | semidirect |
| 179. #103 | C2×D17 | semidirect |
| 182. C17 | #3010 | semidirect |
| 200. C2×Q8 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587694 | 2 |
| C2×#10587594 | 2 |
| C22×#63230 | 2 |
| #11763378 | 2 |
| #11762957 | 2 |
| #11762949 | 2 |
| #11762803 | 2 |
| #11762777 | 2 |
| C17×#419 | 2 |
| #3010 | 17 |