Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
778 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 778 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. #11763801 | C2 | semidirect |
| 4. #11763800 | C2 | semidirect |
| 5. #11763799 | C2 | semidirect |
| 6. C2×#10587547 | C2 | semidirect |
| 8. C17×H(5,𝔽2) | C4 | semidirect |
| 10. #10587696 | C4 | semidirect |
| 11. #10587696 | C4 | semidirect |
| 16. #10587691 | C4 | semidirect |
| 23. #10587677 | C22 | semidirect |
| 24. C2×C4⋊#595 | C22 | semidirect |
| 25. D17⋊M16 | C22 | semidirect |
| 26. C2×#63242 | C22 | semidirect |
| 27. #10587549 | C22 | semidirect |
| 28. #10587549 | C22 | semidirect |
| 29. #10587547 | C22 | semidirect |
| 30. #10587547 | C22 | semidirect |
| 31. #10587547 | C22 | semidirect |
| 36. #41×C17 | C2×C4 | semidirect |
| 38. C2×D4×C17 | C2×C4 | semidirect |
| 42. #63256 | C2×C4 | semidirect |
| 48. #63254 | C2×C4 | semidirect |
| 56. D4×D17 | C2×C4 | semidirect |
| 62. #63252 | C2×C4 | semidirect |
| 64. C2×D68 | C2×C4 | semidirect |
| 159. H(5,𝔽2) | #595 | semidirect |
| 178. C17 | #2897 | semidirect |
| 193. #41 | C2×#595 | semidirect |
| 210. C2×D4 | 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 |
| #11763801 | 2 |
| #11763800 | 2 |
| #11763799 | 2 |
| C2×#10587547 | 2 |
| H(5,𝔽2)×D17 | 2 |
| #2897 | 17 |