Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #11763284 | C2 | semidirect |
| 3. #11763283 | C2 | semidirect |
| 4. #11762918 | C2 | semidirect |
| 5. #11762889 | C2 | semidirect |
| 6. #11762845 | C2 | semidirect |
| 7. #11762815 | C2 | semidirect |
| 8. #11762767 | C2 | semidirect |
| 9. C17×#418 | C2 | semidirect |
| 16. D4×Dic17 | C22 | semidirect |
| 17. C2×#63228 | C4 | semidirect |
| 23. #10587579 | C22 | semidirect |
| 26. C17×#102 | C22 | semidirect |
| 27. #10587492 | C22 | semidirect |
| 28. #10587486 | C22 | semidirect |
| 29. C8×Dic17 | C22 | semidirect |
| 30. #10587479 | C22 | semidirect |
| 31. #10587478 | C22 | semidirect |
| 36. C2×D4×C17 | C2×C4 | semidirect |
| 42. C2×D68 | C2×C4 | semidirect |
| 53. #63228 | C2×C4 | semidirect |
| 54. #63228 | C2×C4 | semidirect |
| 60. C2×#3622 | C2×C4 | semidirect |
| 111. #418 | D17 | semidirect |
| 137. #102 | C2×D17 | semidirect |
| 140. C17 | #2948 | semidirect |
| 149. C2×D4 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63228 | 2 |
| #11763284 | 2 |
| #11763283 | 2 |
| #11762918 | 2 |
| #11762889 | 2 |
| #11762845 | 2 |
| #11762815 | 2 |
| #11762767 | 2 |
| C17×#418 | 2 |
| #2948 | 17 |