Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
280 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 52 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. D17⋊#100 | C2 | semidirect |
| 2. D17⋊#99 | C2 | semidirect |
| 3. #11763711 | C2 | semidirect |
| 4. #11763710 | C2 | semidirect |
| 7. C22×D68 | C4 | semidirect |
| 10. C17×#123 | C4 | semidirect |
| 11. #10587623 | C4 | semidirect |
| 18. C22⋊C4×D17 | C4 | semidirect |
| 24. C23×D17 | C2×C4 | semidirect |
| 28. C22×C4×C17 | C2×C4 | semidirect |
| 49. C22⋊C4×C17 | C2×C4 | semidirect |
| 50. C22⋊Dic17 | C2×C4 | semidirect |
| 137. #123 | #595 | semidirect |
| 149. C17 | #2121 | semidirect |
| 168. C22×C4 | C2×#595 | semidirect |
| 182. C22⋊C4 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#100 | 2 |
| D17⋊#99 | 2 |
| #11763711 | 2 |
| #11763710 | 2 |
| #11763370 | 2 |
| #2121 | 17 |