Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763380 | C2 | semidirect |
| 2. #11763150 | C2 | semidirect |
| 3. #11763130 | C2 | semidirect |
| 4. #11763053 | C2 | semidirect |
| 5. #11763036 | C2 | semidirect |
| 6. #11762960 | C2 | semidirect |
| 7. #11762947 | C2 | semidirect |
| 8. #11762776 | C2 | semidirect |
| 12. C22×Dic34 | C22 | semidirect |
| 26. #10587612 | C22 | semidirect |
| 28. #10587610 | C22 | semidirect |
| 29. C2×#63223 | C22 | semidirect |
| 30. C22×#3622 | C22 | semidirect |
| 34. C22⋊#3622 | C22 | semidirect |
| 35. #10587481 | C22 | semidirect |
| 36. #10587481 | C22 | semidirect |
| 37. #10587479 | C22 | semidirect |
| 38. #10587478 | C22 | semidirect |
| 176. C17 | #3200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763380 | 2 |
| #11763150 | 2 |
| #11763130 | 2 |
| #11763053 | 2 |
| #11763036 | 2 |
| #11762960 | 2 |
| #11762947 | 2 |
| #11762776 | 2 |
| C17×#535 | 2 |
| #3200 | 17 |