Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
832 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
|---|---|---|
| 2. C2×C4×C22⋊D17 | C2 | semidirect |
| 3. C2×#10587567 | C2 | semidirect |
| 4. #11762709 | C2 | semidirect |
| 5. #11762709 | C2 | semidirect |
| 6. #11762689 | C2 | semidirect |
| 7. #11762687 | C2 | semidirect |
| 8. #11762660 | C2 | semidirect |
| 9. C17×#386 | C2 | semidirect |
| 21. #10587626 | C4 | semidirect |
| 39. C2×D4×C17 | C2×C4 | semidirect |
| 49. C2×C22⋊D17 | C2×C4 | semidirect |
| 50. C2×C22⋊D17 | C2×C4 | semidirect |
| 58. C2×D68 | C2×C4 | semidirect |
| 70. #63225 | D4 | semidirect |
| 73. C4×Dic17 | C2×C4 | semidirect |
| 145. Dic17 | C4×D4 | semidirect |
| 153. #386 | D17 | semidirect |
| 187. C17 | #2366 | semidirect |
| 202. C2×D4 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587626 | 2 |
| C2×C4×C22⋊D17 | 2 |
| C2×#10587567 | 2 |
| #11762709 | 2 |
| #11762689 | 2 |
| #11762687 | 2 |
| #11762660 | 2 |
| C17×#386 | 2 |
| #2366 | 17 |