Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #11763106 | C2 | semidirect |
| 3. #11763106 | C2 | semidirect |
| 4. #11763096 | C2 | semidirect |
| 5. #11763086 | C2 | semidirect |
| 6. #11762849 | C2 | semidirect |
| 7. #11762845 | C2 | semidirect |
| 8. #11762836 | C2 | semidirect |
| 11. C17×#544 | C2 | semidirect |
| 14. C17×C4⋊Q8 | C22 | semidirect |
| 16. C17×#125 | C22 | semidirect |
| 33. #10587479 | C22 | semidirect |
| 34. #10587479 | C22 | semidirect |
| 35. #10587479 | C22 | semidirect |
| 36. #10587478 | C22 | semidirect |
| 37. #10587478 | C22 | semidirect |
| 38. #10587478 | C22 | semidirect |
| 39. C4⋊#3622 | C22 | semidirect |
| 40. C4⋊#3622 | C22 | semidirect |
| 47. C2×D68 | Q8 | semidirect |
| 120. #544 | D17 | semidirect |
| 140. C4⋊Q8 | C2×D17 | semidirect |
| 142. #125 | C2×D17 | semidirect |
| 165. C17 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763283 | 2 |
| #11763106 | 2 |
| #11763096 | 2 |
| #11763086 | 2 |
| #11762849 | 2 |
| #11762845 | 2 |
| #11762836 | 2 |
| #11762813 | 2 |
| C2×#10587480 | 2 |
| C17×#544 | 2 |
| #3081 | 17 |