Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#63229 | C2 | semidirect |
| 2. #11763380 | C2 | semidirect |
| 3. #11763284 | C2 | semidirect |
| 4. #11763022 | C2 | semidirect |
| 5. #11763012 | C2 | semidirect |
| 6. #11762837 | C2 | semidirect |
| 7. #11762819 | C2 | semidirect |
| 8. #11762805 | C2 | semidirect |
| 18. #10587630 | C22 | semidirect |
| 19. #10587622 | C22 | semidirect |
| 29. #10587506 | C22 | semidirect |
| 30. #10587503 | C22 | semidirect |
| 31. #10587487 | C22 | semidirect |
| 32. #10587485 | C22 | semidirect |
| 149. C17 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63229 | 2 |
| #11763380 | 2 |
| #11763284 | 2 |
| #11763022 | 2 |
| #11763012 | 2 |
| #11762837 | 2 |
| #11762819 | 2 |
| #11762805 | 2 |
| C2×C17×AGL(1,ℤ/8) | 2 |
| #3042 | 17 |