Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#63230 | C2 | semidirect |
| 3. #11763287 | C2 | semidirect |
| 4. #11763033 | C2 | semidirect |
| 5. #11763007 | C2 | semidirect |
| 6. #11762837 | C2 | semidirect |
| 7. #11762815 | C2 | semidirect |
| 8. #11762805 | C2 | semidirect |
| 9. C2×C17×#137 | C2 | semidirect |
| 14. C2×Q16×C17 | C22 | semidirect |
| 15. C2×SD16×C17 | C22 | semidirect |
| 19. Q8×Dic17 | C22 | semidirect |
| 29. #10587506 | C22 | semidirect |
| 30. #10587503 | C22 | semidirect |
| 32. #10587485 | C22 | semidirect |
| 38. C2×Q8×C17 | D4 | semidirect |
| 112. C2×#137 | D17 | semidirect |
| 130. C2×Q16 | C2×D17 | semidirect |
| 133. C2×SD16 | C2×D17 | semidirect |
| 149. C17 | #3043 | semidirect |
| 155. C2×Q8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63230 | 2 |
| #11763373 | 2 |
| #11763287 | 2 |
| #11763033 | 2 |
| #11763007 | 2 |
| #11762837 | 2 |
| #11762815 | 2 |
| #11762805 | 2 |
| C2×C17×#137 | 2 |
| #3043 | 17 |