Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11763533 | C2 | semidirect |
| 3. #11763132 | C2 | semidirect |
| 4. #11763086 | C2 | semidirect |
| 5. #11763054 | C2 | semidirect |
| 6. #11763006 | C2 | semidirect |
| 7. #11762961 | C2 | semidirect |
| 8. C4×#63219 | C2 | semidirect |
| 9. #11762888 | C2 | semidirect |
| 10. #11762812 | C2 | semidirect |
| 11. C17×#486 | C2 | semidirect |
| 14. C17×C4⋊Q8 | C22 | semidirect |
| 21. C2×#63229 | C22 | semidirect |
| 23. C2×#63218 | C22 | semidirect |
| 25. #10587583 | C22 | semidirect |
| 26. #10587578 | C22 | semidirect |
| 29. C4×Dic34 | C22 | semidirect |
| 30. C17×#102 | C22 | semidirect |
| 31. C17×#102 | C22 | semidirect |
| 32. C4×C8×C17 | C22 | semidirect |
| 33. #10587503 | C22 | semidirect |
| 35. #10587491 | C22 | semidirect |
| 36. #10587488 | C22 | semidirect |
| 37. #10587487 | C22 | semidirect |
| 39. #10587478 | C22 | semidirect |
| 40. C4⋊#3622 | C22 | semidirect |
| 132. #486 | D17 | semidirect |
| 152. C4⋊Q8 | C2×D17 | semidirect |
| 172. #102 | C2×D17 | semidirect |
| 173. #102 | C2×D17 | semidirect |
| 175. C4×C8 | C2×D17 | semidirect |
| 176. C17 | #3324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763533 | 2 |
| #11763444 | 2 |
| #11763132 | 2 |
| #11763086 | 2 |
| #11763054 | 2 |
| #11763006 | 2 |
| #11762961 | 2 |
| C4×#63219 | 2 |
| #11762888 | 2 |
| #11762812 | 2 |
| C17×#486 | 2 |
| #3324 | 17 |