Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. C2×#10587630 | C2 | semidirect |
| 5. #11763013 | C2 | direct (N × H) |
| 6. C2×#10587485 | C2 | semidirect |
| 7. C2×#10587481 | C2 | semidirect |
| 8. C2×C17×#103 | C2 | semidirect |
| 16. #10587630 | C22 | semidirect |
| 28. C17×#103 | C22 | semidirect |
| 29. #10587485 | C22 | semidirect |
| 30. #10587481 | C22 | semidirect |
| 84. C2×Dic17 | SD16 | semidirect |
| 112. Dic17 | C2×SD16 | semidirect |
| 120. C2×#103 | D17 | semidirect |
| 121. C2×C17 | #461 | semidirect |
| 147. #103 | C2×D17 | semidirect |
| 148. C17 | C2×#461 | semidirect |
| 231. C2 | #11763013 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63219 | 2 |
| C22×#63230 | 2 |
| C2×#10587630 | 2 |
| C2×#10587579 | 2 |
| #11763013 | 2 |
| C2×#10587485 | 2 |
| C2×#10587481 | 2 |
| C2×C17×#103 | 2 |
| C2×#461 | 17 |