Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11763520 | C2 | semidirect |
| 3. #11763126 | C2 | semidirect |
| 4. #11763096 | C2 | semidirect |
| 5. #11763037 | C2 | semidirect |
| 6. #11763006 | C2 | semidirect |
| 7. #11762961 | C2 | semidirect |
| 8. C4×#63219 | C2 | semidirect |
| 9. C8×D68 | C2 | semidirect |
| 10. #102×D17 | C2 | semidirect |
| 11. C17×#486 | C2 | semidirect |
| 14. C17×C4⋊Q8 | C22 | semidirect |
| 20. C2×#63229 | C22 | semidirect |
| 22. C2×C8×D17 | C22 | semidirect |
| 23. #10587583 | C22 | semidirect |
| 25. C4⋊C4×D17 | C22 | semidirect |
| 29. C4×Dic34 | C22 | semidirect |
| 30. C17×#102 | C22 | semidirect |
| 31. C17×#102 | C22 | semidirect |
| 32. C4×C8×C17 | C22 | semidirect |
| 33. #10587503 | C22 | semidirect |
| 35. #10587491 | C22 | semidirect |
| 36. #10587488 | C22 | semidirect |
| 37. #10587487 | C22 | semidirect |
| 39. #10587479 | C22 | semidirect |
| 40. C4⋊#3622 | C22 | semidirect |
| 99. D68 | SD16 | semidirect |
| 133. #486 | D17 | semidirect |
| 153. C4⋊Q8 | C2×D17 | semidirect |
| 173. #102 | C2×D17 | semidirect |
| 174. #102 | C2×D17 | semidirect |
| 176. C4×C8 | C2×D17 | semidirect |
| 177. C17 | #3295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763520 | 2 |
| #11763444 | 2 |
| #11763126 | 2 |
| #11763096 | 2 |
| #11763037 | 2 |
| #11763006 | 2 |
| #11762961 | 2 |
| C4×#63219 | 2 |
| C8×D68 | 2 |
| #102×D17 | 2 |
| C17×#486 | 2 |
| #3295 | 17 |