Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
726 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 200 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. #11763878 | C2 | semidirect |
| 3. #11763802 | C2 | semidirect |
| 4. #11763800 | C2 | semidirect |
| 5. #11763799 | C2 | semidirect |
| 6. C2×#10587549 | C2 | semidirect |
| 8. C17×2−1+4 | C4 | semidirect |
| 10. #10587697 | C4 | semidirect |
| 11. #10587697 | C4 | semidirect |
| 16. #10587694 | C4 | semidirect |
| 35. #41×C17 | C2×C4 | semidirect |
| 37. C2×Q8×C17 | C2×C4 | semidirect |
| 39. #63256 | C2×C4 | semidirect |
| 45. Q8×D17 | C2×C4 | semidirect |
| 51. #63254 | C2×C4 | semidirect |
| 60. #63252 | C2×C4 | semidirect |
| 66. C2×Dic34 | C2×C4 | semidirect |
| 154. 2−1+4 | #595 | semidirect |
| 173. C17 | #2898 | semidirect |
| 189. #41 | C2×#595 | semidirect |
| 201. C2×Q8 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#131 | 2 |
| #11763878 | 2 |
| #11763802 | 2 |
| #11763800 | 2 |
| #11763799 | 2 |
| C2×#10587549 | 2 |
| 2−1+4×D17 | 2 |
| #2898 | 17 |