Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763440 | C2 | semidirect |
| 3. #11763172 | C2 | semidirect |
| 4. #11763167 | C2 | semidirect |
| 5. #11763162 | C2 | semidirect |
| 6. #11763154 | C2 | semidirect |
| 7. #11762814 | C2 | semidirect |
| 8. #11762808 | C2 | semidirect |
| 9. #11762806 | C2 | semidirect |
| 10. #11762764 | C2 | semidirect |
| 11. C2×C17×#102 | C2 | semidirect |
| 26. #10587576 | C22 | semidirect |
| 28. #10587574 | C22 | semidirect |
| 33. #10587492 | C22 | semidirect |
| 34. #10587492 | C22 | semidirect |
| 35. #10587487 | C22 | semidirect |
| 36. #10587487 | C22 | semidirect |
| 37. #10587486 | C22 | semidirect |
| 38. C8×Dic17 | C22 | semidirect |
| 39. #10587481 | C22 | semidirect |
| 40. #10587480 | C22 | semidirect |
| 139. C2×#102 | D17 | semidirect |
| 176. C17 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763440 | 2 |
| #11763376 | 2 |
| #11763172 | 2 |
| #11763167 | 2 |
| #11763162 | 2 |
| #11763154 | 2 |
| #11762814 | 2 |
| #11762808 | 2 |
| #11762806 | 2 |
| #11762764 | 2 |
| C2×C17×#102 | 2 |
| #3136 | 17 |