Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10587594 | C2 | semidirect |
| 2. C2×#10587636 | C2 | semidirect |
| 3. #11763373 | C2 | semidirect |
| 4. #11763290 | C2 | semidirect |
| 5. #11763034 | C2 | semidirect |
| 6. #11763027 | C2 | semidirect |
| 7. #11763008 | C2 | semidirect |
| 8. #11763003 | C2 | semidirect |
| 9. #11762837 | C2 | semidirect |
| 10. C2×#10587480 | C2 | semidirect |
| 11. C17×#417 | C2 | semidirect |
| 19. C2×#63231 | C22 | semidirect |
| 20. C2×#63230 | C22 | semidirect |
| 23. C2×#63229 | C22 | semidirect |
| 24. C2×#63228 | C22 | semidirect |
| 33. #10587579 | C22 | semidirect |
| 36. #10587573 | C22 | semidirect |
| 37. C17×#103 | C22 | semidirect |
| 38. C17×#102 | C22 | semidirect |
| 39. #10587485 | C22 | semidirect |
| 40. #10587485 | C22 | semidirect |
| 56. #63252 | D4 | semidirect |
| 157. #417 | D17 | semidirect |
| 193. #103 | C2×D17 | semidirect |
| 196. #102 | C2×D17 | semidirect |
| 197. C17 | #3045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587594 | 2 |
| C2×#10587636 | 2 |
| #11763373 | 2 |
| #11763290 | 2 |
| #11763034 | 2 |
| #11763027 | 2 |
| #11763008 | 2 |
| #11763003 | 2 |
| #11762837 | 2 |
| C2×#10587480 | 2 |
| C17×#417 | 2 |
| #3045 | 17 |