Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#63228 | C2 | semidirect |
| 3. #11763378 | C2 | semidirect |
| 4. #11763024 | C2 | semidirect |
| 5. #11763004 | C2 | semidirect |
| 6. #11762836 | C2 | semidirect |
| 7. #11762813 | C2 | semidirect |
| 8. #11762803 | C2 | semidirect |
| 9. C17×#518 | C2 | semidirect |
| 14. C4×D4×C17 | C22 | semidirect |
| 18. C2×#63229 | C22 | semidirect |
| 22. C2×#63228 | C22 | semidirect |
| 27. #10587561 | C22 | semidirect |
| 28. #10587560 | C22 | semidirect |
| 29. #10587481 | C22 | semidirect |
| 30. #10587480 | C22 | semidirect |
| 31. #10587480 | C22 | semidirect |
| 32. C4⋊#3622 | C22 | semidirect |
| 37. C2×D4×C17 | D4 | semidirect |
| 119. #518 | D17 | semidirect |
| 146. C4×D4 | C2×D17 | semidirect |
| 154. C17 | #3041 | semidirect |
| 169. C2×D4 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587618 | 2 |
| C22×#63228 | 2 |
| #11763378 | 2 |
| #11763024 | 2 |
| #11763004 | 2 |
| #11762836 | 2 |
| #11762813 | 2 |
| #11762803 | 2 |
| C17×#518 | 2 |
| #3041 | 17 |