Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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. #11762744 | C2 | semidirect |
| 3. #11762731 | C2 | semidirect |
| 4. #11762720 | C2 | semidirect |
| 5. #11762681 | C2 | semidirect |
| 6. #11762669 | C2 | semidirect |
| 8. C2×C17×C22⋊Q8 | C2 | semidirect |
| 10. C22×Q8×C17 | C22 | semidirect |
| 14. C2×C4⋊C4×C17 | C22 | semidirect |
| 15. C2×C4⋊C4×C17 | C22 | semidirect |
| 23. C2×C4⋊Dic17 | C22 | semidirect |
| 24. C2×#63225 | C22 | semidirect |
| 25. #10587502 | C22 | semidirect |
| 26. #10587502 | C22 | semidirect |
| 32. C23×D17 | Q8 | semidirect |
| 111. C2×C22⋊Q8 | D17 | semidirect |
| 127. C22×Q8 | C2×D17 | semidirect |
| 133. C2×C4⋊C4 | C2×D17 | semidirect |
| 134. C2×C4⋊C4 | C2×D17 | semidirect |
| 144. C17 | #2626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63227 | 2 |
| #11762744 | 2 |
| #11762731 | 2 |
| #11762720 | 2 |
| #11762681 | 2 |
| #11762669 | 2 |
| #11762664 | 2 |
| C2×C17×C22⋊Q8 | 2 |
| #2626 | 17 |