Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10587594 | C2 | semidirect |
| 2. C2×#10587636 | C2 | semidirect |
| 3. C22×#63228 | C2 | semidirect |
| 4. #11763376 | C2 | semidirect |
| 5. #11763373 | C2 | semidirect |
| 6. #11763197 | C2 | semidirect |
| 7. #11763195 | C2 | semidirect |
| 8. #11763190 | C2 | semidirect |
| 9. #11763184 | C2 | semidirect |
| 10. #11762767 | C2 | semidirect |
| 11. C2×C17×AGL(1,ℤ/8) | C2 | semidirect |
| 17. C2×SD16×C17 | C22 | semidirect |
| 18. C2×D8×C17 | C22 | semidirect |
| 22. #10587633 | C22 | semidirect |
| 23. C2×#63231 | C22 | semidirect |
| 24. C2×#63230 | C22 | semidirect |
| 25. #10587626 | C22 | semidirect |
| 26. #10587626 | C22 | semidirect |
| 29. #10587622 | C22 | semidirect |
| 30. C2×#63229 | C22 | semidirect |
| 34. C2×#63228 | C22 | semidirect |
| 39. C2×D136 | C22 | semidirect |
| 40. C2×#63219 | C22 | semidirect |
| 41. #10587486 | C22 | semidirect |
| 42. C8×Dic17 | C22 | semidirect |
| 70. M16×C17 | D4 | semidirect |
| 83. C2×#3622 | D4 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D17 | semidirect |
| 176. C2×SD16 | C2×D17 | semidirect |
| 182. C2×D8 | C2×D17 | semidirect |
| 196. C17 | #3155 | semidirect |
| 232. M16 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587594 | 2 |
| C2×#10587636 | 2 |
| C22×#63228 | 2 |
| #11763376 | 2 |
| #11763373 | 2 |
| #11763197 | 2 |
| #11763195 | 2 |
| #11763190 | 2 |
| #11763184 | 2 |
| #11762767 | 2 |
| C2×C17×AGL(1,ℤ/8) | 2 |
| #3155 | 17 |