Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
332 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 68 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⋊#131 | C2 | semidirect |
| 2. #11763800 | C2 | semidirect |
| 3. C2×#10587547 | C2 | semidirect |
| 4. D17⋊#100 | C2 | semidirect |
| 5. #11763688 | C2 | semidirect |
| 6. #11763684 | C2 | semidirect |
| 19. C17×AGL(1,ℤ/8) | C4 | semidirect |
| 20. #10587635 | C4 | semidirect |
| 21. #10587618 | C4 | semidirect |
| 26. #10587594 | C4 | semidirect |
| 171. AGL(1,ℤ/8) | #595 | semidirect |
| 189. C17 | #1907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#131 | 2 |
| #11763800 | 2 |
| C2×#10587547 | 2 |
| D17⋊#100 | 2 |
| #11763688 | 2 |
| #11763684 | 2 |
| AGL(1,ℤ/8)×D17 | 2 |
| #1907 | 17 |