Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763290 | C2 | semidirect |
| 3. #11763136 | C2 | semidirect |
| 4. #11763135 | C2 | semidirect |
| 5. #11763129 | C2 | semidirect |
| 6. #11763124 | C2 | semidirect |
| 7. #11762845 | C2 | semidirect |
| 8. #11762815 | C2 | semidirect |
| 9. C2×#10587480 | C2 | semidirect |
| 10. #11762777 | C2 | semidirect |
| 11. C17×#428 | C2 | semidirect |
| 23. #10587578 | C22 | semidirect |
| 24. C4⋊C4×D17 | C22 | semidirect |
| 29. C17×#107 | C22 | semidirect |
| 30. C17×#106 | C22 | semidirect |
| 33. #10587491 | C22 | semidirect |
| 34. #10587491 | C22 | semidirect |
| 37. #10587479 | C22 | semidirect |
| 38. #10587479 | C22 | semidirect |
| 39. #10587478 | C22 | semidirect |
| 40. #10587478 | C22 | semidirect |
| 135. #428 | D17 | semidirect |
| 165. #107 | C2×D17 | semidirect |
| 168. #106 | C2×D17 | semidirect |
| 175. C17 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763378 | 2 |
| #11763290 | 2 |
| #11763136 | 2 |
| #11763135 | 2 |
| #11763129 | 2 |
| #11763124 | 2 |
| #11762845 | 2 |
| #11762815 | 2 |
| C2×#10587480 | 2 |
| #11762777 | 2 |
| C17×#428 | 2 |
| #3096 | 17 |