Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11763340 | C2 | semidirect |
| 2. C2×#10587633 | C2 | semidirect |
| 3. #11763190 | C2 | semidirect |
| 4. #11763165 | C2 | semidirect |
| 5. #11763034 | C2 | semidirect |
| 6. #11763026 | C2 | semidirect |
| 7. #11762965 | C2 | semidirect |
| 8. #11762962 | C2 | semidirect |
| 10. #11762859 | C2 | semidirect |
| 11. C17×#448 | C2 | semidirect |
| 14. C2×SD16×C17 | C22 | semidirect |
| 20. C2×#63231 | C22 | semidirect |
| 21. #10587622 | C22 | semidirect |
| 24. D4×Dic17 | C22 | semidirect |
| 31. #10587576 | C22 | semidirect |
| 32. #10587573 | C22 | semidirect |
| 35. C17×#103 | C22 | semidirect |
| 37. #10587506 | C22 | semidirect |
| 40. #10587485 | C22 | semidirect |
| 41. C8×Dic17 | C22 | semidirect |
| 146. #448 | D17 | semidirect |
| 159. C2×SD16 | C2×D17 | semidirect |
| 180. #103 | C2×D17 | semidirect |
| 186. C17 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763340 | 2 |
| C2×#10587633 | 2 |
| #11763190 | 2 |
| #11763165 | 2 |
| #11763034 | 2 |
| #11763026 | 2 |
| #11762965 | 2 |
| #11762962 | 2 |
| #11762942 | 2 |
| #11762859 | 2 |
| C17×#448 | 2 |
| #3211 | 17 |