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×#10587635 | C2 | semidirect |
| 2. C22×D136 | C2 | semidirect |
| 3. #11763373 | C2 | semidirect |
| 4. #11763195 | C2 | semidirect |
| 5. #11763194 | C2 | semidirect |
| 6. #11763184 | C2 | semidirect |
| 7. #11762764 | C2 | semidirect |
| 8. C2×C17×#135 | C2 | semidirect |
| 12. C2×Q16×C17 | C22 | semidirect |
| 13. C2×SD16×C17 | C22 | semidirect |
| 14. C2×D8×C17 | C22 | semidirect |
| 17. #10587633 | C22 | semidirect |
| 18. C2×#63230 | C22 | semidirect |
| 19. #10587626 | C22 | semidirect |
| 21. C2×#63228 | C22 | semidirect |
| 28. #10587486 | C22 | semidirect |
| 29. C8×Dic17 | C22 | semidirect |
| 46. C2×C8×C17 | D4 | semidirect |
| 55. #63223 | D4 | semidirect |
| 98. C2×#135 | D17 | semidirect |
| 114. C2×Q16 | C2×D17 | semidirect |
| 116. C2×SD16 | C2×D17 | semidirect |
| 121. C2×D8 | C2×D17 | semidirect |
| 131. C17 | #3155 | semidirect |
| 154. C2×C8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587635 | 2 |
| C22×D136 | 2 |
| #11763373 | 2 |
| #11763195 | 2 |
| #11763194 | 2 |
| #11763184 | 2 |
| #11762764 | 2 |
| C2×C17×#135 | 2 |
| #3155 | 17 |