Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
286 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 286 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⋊#99 | C2 | semidirect |
| 2. #11763715 | C2 | semidirect |
| 3. #11763714 | C2 | semidirect |
| 5. C2×#63256 | C4 | semidirect |
| 8. C17×#124 | C4 | semidirect |
| 10. #10587626 | C4 | semidirect |
| 14. #10587558 | C4 | semidirect |
| 19. C2×Q8×C17 | C2×C4 | semidirect |
| 27. C2×D68 | C2×C4 | semidirect |
| 34. C42×C17 | C2×C4 | semidirect |
| 38. C4×Dic17 | C2×C4 | semidirect |
| 96. #124 | #595 | semidirect |
| 103. C17 | #2127 | semidirect |
| 106. C2×Q8 | C2×#595 | semidirect |
| 125. C42 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#99 | 2 |
| #11763715 | 2 |
| #11763714 | 2 |
| #11763377 | 2 |
| #2127 | 17 |