Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 2. #11762882 | C2 | semidirect |
| 3. #11762879 | C2 | semidirect |
| 4. C8×D68 | C2 | semidirect |
| 5. #11762874 | C2 | semidirect |
| 6. #11762870 | C2 | semidirect |
| 7. #11762774 | C2 | semidirect |
| 8. C22⋊C8×D17 | C2 | semidirect |
| 9. C17×#433 | C2 | semidirect |
| 13. C2×#63218 | C22 | semidirect |
| 16. C2×C8×D17 | C22 | semidirect |
| 23. C17×C4⋊C8 | C22 | semidirect |
| 25. C17×#97 | C22 | semidirect |
| 26. C4×C8×C17 | C22 | semidirect |
| 30. #10587491 | C22 | semidirect |
| 31. #10587491 | C22 | semidirect |
| 32. C4⋊#3622 | C22 | semidirect |
| 33. #10587474 | C22 | semidirect |
| 34. C4×#3622 | C22 | semidirect |
| 116. #433 | D17 | semidirect |
| 138. C4⋊C8 | C2×D17 | semidirect |
| 146. #97 | C2×D17 | semidirect |
| 148. C4×C8 | C2×D17 | semidirect |
| 149. C17 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763321 | 2 |
| #11762882 | 2 |
| #11762879 | 2 |
| C8×D68 | 2 |
| #11762874 | 2 |
| #11762870 | 2 |
| #11762774 | 2 |
| C22⋊C8×D17 | 2 |
| C17×#433 | 2 |
| #2977 | 17 |