Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11763422 | C2 | semidirect |
| 3. #11763204 | C2 | semidirect |
| 4. #11763182 | C2 | semidirect |
| 5. #11763175 | C2 | semidirect |
| 6. #11763034 | C2 | semidirect |
| 7. #11763008 | C2 | semidirect |
| 8. #11762974 | C2 | semidirect |
| 9. #11762961 | C2 | semidirect |
| 10. #11762868 | C2 | semidirect |
| 11. C17×#488 | C2 | semidirect |
| 14. C17×#125 | C22 | semidirect |
| 17. C2×#63231 | C22 | semidirect |
| 21. C2×#63219 | C22 | semidirect |
| 25. #10587573 | C22 | semidirect |
| 30. #10587555 | C22 | semidirect |
| 31. C17×#103 | C22 | semidirect |
| 33. C4×C8×C17 | C22 | semidirect |
| 35. #10587485 | C22 | semidirect |
| 37. #10587480 | C22 | semidirect |
| 38. #10587474 | C22 | semidirect |
| 122. #488 | D17 | semidirect |
| 145. #125 | C2×D17 | semidirect |
| 154. #103 | C2×D17 | semidirect |
| 160. C4×C8 | 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 |
|---|---|
| #11763422 | 2 |
| #11763377 | 2 |
| #11763204 | 2 |
| #11763182 | 2 |
| #11763175 | 2 |
| #11763034 | 2 |
| #11763008 | 2 |
| #11762974 | 2 |
| #11762961 | 2 |
| #11762868 | 2 |
| C17×#488 | 2 |
| #3222 | 17 |