Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 2. C2×#10587630 | C2 | semidirect |
| 3. #11763180 | C2 | semidirect |
| 4. #11763158 | C2 | semidirect |
| 5. #11763013 | C2 | semidirect |
| 6. #11763012 | C2 | semidirect |
| 7. #11762950 | C2 | semidirect |
| 8. #11762948 | C2 | semidirect |
| 9. #11762947 | C2 | semidirect |
| 10. #11762859 | C2 | semidirect |
| 11. C17×#448 | C2 | semidirect |
| 107. C2×Dic17 | SD16 | semidirect |
| 150. #448 | D17 | semidirect |
| 189. C17 | #3206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763354 | 2 |
| C2×#10587630 | 2 |
| #11763180 | 2 |
| #11763158 | 2 |
| #11763013 | 2 |
| #11763012 | 2 |
| #11762950 | 2 |
| #11762948 | 2 |
| #11762947 | 2 |
| #11762859 | 2 |
| C17×#448 | 2 |
| #3206 | 17 |