Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 2. #11763150 | C2 | semidirect |
| 3. #11763144 | C2 | semidirect |
| 4. #11763133 | C2 | semidirect |
| 5. #11763122 | C2 | semidirect |
| 6. #11762852 | C2 | semidirect |
| 7. C2×#10587478 | C2 | semidirect |
| 8. #11762808 | C2 | semidirect |
| 9. #11762803 | C2 | semidirect |
| 10. #11762776 | C2 | semidirect |
| 11. C17×#520 | C2 | semidirect |
| 129. #520 | D17 | semidirect |
| 174. C17 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763387 | 2 |
| #11763150 | 2 |
| #11763144 | 2 |
| #11763133 | 2 |
| #11763122 | 2 |
| #11762852 | 2 |
| C2×#10587478 | 2 |
| #11762808 | 2 |
| #11762803 | 2 |
| #11762776 | 2 |
| C17×#520 | 2 |
| #3098 | 17 |