Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
280 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 65 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×#10587505 | C2 | semidirect |
| 3. #11762600 | C2 | semidirect |
| 4. #11762597 | C2 | semidirect |
| 5. C2×C17×#100 | C2 | semidirect |
| 7. C22×C22⋊D17 | C4 | semidirect |
| 11. C2×C22⋊Dic17 | C4 | semidirect |
| 14. #10587623 | C4 | semidirect |
| 16. #10587621 | C4 | semidirect |
| 25. C23×D17 | C2×C4 | semidirect |
| 41. C22×Dic17 | C2×C4 | semidirect |
| 50. C22⋊Dic17 | C2×C4 | semidirect |
| 51. C22⋊Dic17 | C2×C4 | semidirect |
| 119. C2×#100 | D17 | semidirect |
| 149. C17 | #2121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763368 | 2 |
| C2×#10587505 | 2 |
| #11762600 | 2 |
| #11762597 | 2 |
| C2×C17×#100 | 2 |
| #2121 | 17 |