Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 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 |
|---|---|---|
| 1. C23×D68 | C2 | semidirect |
| 2. C2×#10587594 | C2 | semidirect |
| 3. #11763320 | C2 | semidirect |
| 4. #11762962 | C2 | semidirect |
| 5. #11762945 | C2 | semidirect |
| 6. #11762815 | C2 | semidirect |
| 7. C17×#407 | C2 | semidirect |
| 10. C2×#63252 | C22 | semidirect |
| 16. C2×M16×C17 | C22 | semidirect |
| 18. #10587616 | C22 | semidirect |
| 21. #10587612 | C22 | semidirect |
| 22. #10587610 | C22 | semidirect |
| 24. C2×D136 | C22 | semidirect |
| 25. C2×#63219 | C22 | semidirect |
| 26. C17×C22⋊C8 | C22 | semidirect |
| 27. #10587492 | C22 | semidirect |
| 47. C2×D68 | D4 | semidirect |
| 49. C2×D68 | C23 | semidirect |
| 51. C2×Dic34 | C23 | semidirect |
| 53. C2×C8×C17 | C23 | semidirect |
| 57. C4⋊Dic17 | C23 | semidirect |
| 99. C22×C17 | AGL(1,ℤ/8) | semidirect |
| 118. #407 | D17 | semidirect |
| 136. C2×M16 | C2×D17 | semidirect |
| 144. C22⋊C8 | C2×D17 | semidirect |
| 145. C17 | #3003 | semidirect |
| 173. C2×C8 | C22×D17 | semidirect |
| 222. C22 | #10587594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D68 | 2 |
| C2×#10587594 | 2 |
| #11763320 | 2 |
| #11762962 | 2 |
| #11762945 | 2 |
| #11762815 | 2 |
| C17×#407 | 2 |
| #3003 | 17 |