Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 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. #11763440 | C2 | semidirect |
| 3. #11763112 | C2 | semidirect |
| 4. #11763108 | C2 | semidirect |
| 5. #11763098 | C2 | semidirect |
| 6. #11763088 | C2 | semidirect |
| 7. #11762845 | C2 | semidirect |
| 8. #11762837 | C2 | semidirect |
| 11. C17×#428 | C2 | semidirect |
| 23. #10587576 | C22 | semidirect |
| 25. #10587574 | C22 | semidirect |
| 29. C17×#107 | C22 | semidirect |
| 30. C17×#106 | C22 | semidirect |
| 33. #10587485 | C22 | semidirect |
| 34. #10587485 | C22 | semidirect |
| 37. #10587479 | C22 | semidirect |
| 38. #10587479 | C22 | semidirect |
| 39. #10587478 | C22 | semidirect |
| 40. #10587478 | C22 | semidirect |
| 46. C2×D68 | Q8 | semidirect |
| 126. #428 | D17 | semidirect |
| 155. #107 | C2×D17 | semidirect |
| 158. #106 | 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 |
|---|---|
| #11763440 | 2 |
| #11763283 | 2 |
| #11763112 | 2 |
| #11763108 | 2 |
| #11763098 | 2 |
| #11763088 | 2 |
| #11762845 | 2 |
| #11762837 | 2 |
| #11762815 | 2 |
| C2×#10587480 | 2 |
| C17×#428 | 2 |
| #3081 | 17 |