Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10587601 | C2 | semidirect |
| 3. C2×Q16×D17 | C2 | semidirect |
| 4. #11763379 | C2 | semidirect |
| 5. #11763204 | C2 | semidirect |
| 6. #11763200 | C2 | semidirect |
| 7. #11763192 | C2 | semidirect |
| 8. #11763189 | C2 | semidirect |
| 9. #11763187 | C2 | semidirect |
| 10. #11762763 | C2 | semidirect |
| 11. C17×#495 | C2 | semidirect |
| 125. #495 | D17 | semidirect |
| 161. C17 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587601 | 2 |
| C2×#10587598 | 2 |
| C2×Q16×D17 | 2 |
| #11763379 | 2 |
| #11763204 | 2 |
| #11763200 | 2 |
| #11763192 | 2 |
| #11763189 | 2 |
| #11763187 | 2 |
| #11762763 | 2 |
| C17×#495 | 2 |
| #3156 | 17 |