Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
738 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 289 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. #11763576 | C2 | semidirect |
| 2. #41×Dic17 | C2 | semidirect |
| 3. #11762826 | C2 | semidirect |
| 4. C2×#10587508 | C2 | semidirect |
| 7. C17×2−1+4 | C4 | semidirect |
| 9. C17×H(5,𝔽2) | C4 | semidirect |
| 16. #10587612 | C22 | semidirect |
| 17. C2×C4×Dic17 | C22 | semidirect |
| 18. C2×#63223 | C22 | semidirect |
| 19. #10587508 | C22 | semidirect |
| 20. #10587508 | C22 | semidirect |
| 26. #41×C17 | C2×C4 | semidirect |
| 30. C2×Q8×C17 | C2×C4 | semidirect |
| 34. C2×D4×C17 | C2×C4 | semidirect |
| 90. 2−1+4 | Dic17 | semidirect |
| 92. H(5,𝔽2) | Dic17 | semidirect |
| 104. C17 | #2901 | semidirect |
| 110. #41 | C2×Dic17 | semidirect |
| 114. C2×Q8 | C2×Dic17 | semidirect |
| 118. C2×D4 | C2×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763576 | 2 |
| #41×Dic17 | 2 |
| #11762826 | 2 |
| C2×#10587508 | 2 |
| C17×#585 | 2 |
| #2901 | 17 |