Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#10587697 | C2 | semidirect |
| 2. #11763609 | C2 | semidirect |
| 3. #11763607 | C2 | semidirect |
| 4. #11763385 | C2 | semidirect |
| 5. #11762993 | C2 | semidirect |
| 6. #11762983 | C2 | semidirect |
| 7. #11762827 | C2 | semidirect |
| 8. C2×#10587495 | C2 | semidirect |
| 9. C17×#421 | C2 | semidirect |
| 25. #10587637 | C22 | semidirect |
| 27. #10587635 | C22 | semidirect |
| 32. #10587595 | C22 | semidirect |
| 34. #10587594 | C22 | semidirect |
| 38. #10587561 | C22 | semidirect |
| 39. #10587555 | C22 | semidirect |
| 40. C17×#104 | C22 | semidirect |
| 41. #10587495 | C22 | semidirect |
| 42. #10587476 | C22 | semidirect |
| 186. #421 | D17 | semidirect |
| 226. #104 | C2×D17 | semidirect |
| 228. C17 | #3020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587697 | 2 |
| #11763609 | 2 |
| #11763607 | 2 |
| #11763385 | 2 |
| #11762993 | 2 |
| #11762983 | 2 |
| #11762827 | 2 |
| C2×#10587495 | 2 |
| C17×#421 | 2 |
| #3020 | 17 |