Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763201 | C2 | semidirect |
| 3. #11763183 | C2 | semidirect |
| 4. #11763175 | C2 | semidirect |
| 5. #11763166 | C2 | semidirect |
| 6. #11763031 | C2 | semidirect |
| 7. #11763009 | C2 | semidirect |
| 8. #11762969 | C2 | semidirect |
| 9. #11762959 | C2 | semidirect |
| 10. #11762870 | C2 | semidirect |
| 11. C17×#541 | C2 | semidirect |
| 14. C17×C4⋊Q8 | C22 | semidirect |
| 17. C17×#125 | C22 | semidirect |
| 19. C4×Q8×C17 | C22 | semidirect |
| 21. C2×#63231 | C22 | semidirect |
| 24. C2×#63230 | C22 | semidirect |
| 32. #10587481 | C22 | semidirect |
| 35. #10587480 | C22 | semidirect |
| 36. C4⋊#3622 | C22 | semidirect |
| 37. #10587474 | C22 | semidirect |
| 38. C4×#3622 | C22 | semidirect |
| 117. #541 | D17 | semidirect |
| 140. C4⋊Q8 | C2×D17 | semidirect |
| 145. #125 | C2×D17 | semidirect |
| 151. C4×Q8 | C2×D17 | semidirect |
| 161. C17 | #3222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763378 | 2 |
| #11763201 | 2 |
| #11763183 | 2 |
| #11763175 | 2 |
| #11763166 | 2 |
| #11763031 | 2 |
| #11763009 | 2 |
| #11762969 | 2 |
| #11762959 | 2 |
| #11762870 | 2 |
| C17×#541 | 2 |
| #3222 | 17 |