Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763364 | C2 | semidirect |
| 3. #11763172 | C2 | semidirect |
| 4. #11763157 | C2 | semidirect |
| 5. #11763156 | C2 | semidirect |
| 6. #11763155 | C2 | semidirect |
| 7. #11762812 | C2 | semidirect |
| 8. C4×#63218 | C2 | semidirect |
| 9. C17×#486 | C2 | semidirect |
| 13. C17×C4⋊Q8 | C22 | semidirect |
| 23. #10587576 | C22 | semidirect |
| 27. #10587555 | C22 | semidirect |
| 28. C17×#102 | C22 | semidirect |
| 29. C4×C8×C17 | C22 | semidirect |
| 30. #10587503 | C22 | semidirect |
| 31. #10587492 | C22 | semidirect |
| 32. #10587486 | C22 | semidirect |
| 33. #10587480 | C22 | semidirect |
| 34. C4×#3622 | C22 | semidirect |
| 124. #486 | D17 | semidirect |
| 138. C4⋊Q8 | C2×D17 | semidirect |
| 154. #102 | C2×D17 | semidirect |
| 157. C4×C8 | C2×D17 | semidirect |
| 158. C17 | #3138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763364 | 2 |
| #127×D17 | 2 |
| #11763172 | 2 |
| #11763157 | 2 |
| #11763156 | 2 |
| #11763155 | 2 |
| #11762812 | 2 |
| C4×#63218 | 2 |
| C17×#486 | 2 |
| #3138 | 17 |