Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
388 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. C2×#10587486 | C2 | semidirect |
| 5. C4⋊C4×Dic17 | C2 | semidirect |
| 6. #11762571 | C2 | semidirect |
| 7. C17×#340 | C2 | semidirect |
| 19. #10587579 | C4 | semidirect |
| 21. #10587492 | C4 | semidirect |
| 23. #10587480 | C4 | semidirect |
| 42. C2×C8×C17 | C2×C4 | semidirect |
| 46. C4⋊C4×C17 | C2×C4 | semidirect |
| 49. C4⋊Dic17 | C2×C4 | semidirect |
| 55. C2×#3622 | C2×C4 | semidirect |
| 88. D68 | C42 | semidirect |
| 122. #340 | D17 | semidirect |
| 147. C17 | #1762 | semidirect |
| 169. C2×C8 | C4×D17 | semidirect |
| 175. C4⋊C4 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587579 | 2 |
| C2×#10587492 | 2 |
| C2×#10587480 | 2 |
| C2×#10587486 | 2 |
| C4⋊C4×Dic17 | 2 |
| #11762571 | 2 |
| C17×#340 | 2 |
| #1762 | 17 |