Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#10587618 | C2 | semidirect |
| 2. C2×#10587590 | C2 | semidirect |
| 3. #11763376 | C2 | semidirect |
| 4. #11763290 | C2 | semidirect |
| 5. #11763030 | C2 | semidirect |
| 6. #11763023 | C2 | semidirect |
| 7. #11763008 | C2 | semidirect |
| 8. #11763003 | C2 | semidirect |
| 9. #11762835 | C2 | semidirect |
| 10. #11762808 | C2 | semidirect |
| 11. C2×C17×#102 | C2 | semidirect |
| 28. C2×Dic68 | C22 | semidirect |
| 30. C2×D136 | C22 | semidirect |
| 31. C2×#63219 | C22 | semidirect |
| 32. C2×#63219 | C22 | semidirect |
| 33. #10587579 | C22 | semidirect |
| 36. #10587573 | C22 | semidirect |
| 39. #10587485 | C22 | semidirect |
| 40. #10587485 | C22 | semidirect |
| 41. #10587481 | C22 | semidirect |
| 42. #10587480 | C22 | semidirect |
| 57. #63252 | D4 | semidirect |
| 158. C2×#102 | D17 | semidirect |
| 197. C17 | #3045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587618 | 2 |
| C2×#10587590 | 2 |
| #11763376 | 2 |
| #11763290 | 2 |
| #11763030 | 2 |
| #11763023 | 2 |
| #11763008 | 2 |
| #11763003 | 2 |
| #11762835 | 2 |
| #11762808 | 2 |
| C2×C17×#102 | 2 |
| #3045 | 17 |