Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 448 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. #11763529 | C2 | semidirect |
| 2. #11763155 | C2 | semidirect |
| 3. #11763130 | C2 | semidirect |
| 4. #11763089 | C2 | semidirect |
| 5. #11763053 | C2 | semidirect |
| 6. #11763006 | C2 | semidirect |
| 7. #11762960 | C2 | semidirect |
| 8. C4×#63229 | C2 | semidirect |
| 9. #11762887 | C2 | semidirect |
| 10. #11762814 | C2 | semidirect |
| 22. C2×#63229 | C22 | semidirect |
| 23. #10587612 | C22 | semidirect |
| 24. #10587610 | C22 | semidirect |
| 25. C2×#63223 | C22 | semidirect |
| 28. #10587555 | C22 | semidirect |
| 29. C4×Dic34 | C22 | semidirect |
| 32. #10587503 | C22 | semidirect |
| 33. #10587503 | C22 | semidirect |
| 34. #10587503 | C22 | semidirect |
| 35. C22⋊#3622 | C22 | semidirect |
| 36. #10587481 | C22 | semidirect |
| 37. #10587479 | C22 | semidirect |
| 38. #10587478 | C22 | semidirect |
| 39. C4⋊#3622 | C22 | semidirect |
| 40. C4×#3622 | C22 | semidirect |
| 176. C17 | #3324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763529 | 2 |
| #11763155 | 2 |
| #11763130 | 2 |
| #11763089 | 2 |
| #11763053 | 2 |
| #11763006 | 2 |
| #11762960 | 2 |
| C4×#63229 | 2 |
| #11762887 | 2 |
| #11762814 | 2 |
| D42×C17 | 2 |
| #3324 | 17 |