Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #11762819 | C2 | semidirect |
| 5. #11762714 | C2 | semidirect |
| 6. #11762570 | C2 | semidirect |
| 7. C17×#343 | C2 | semidirect |
| 17. #10587595 | C4 | semidirect |
| 45. C2×Dic34 | C2×C4 | semidirect |
| 50. M16×C17 | C2×C4 | semidirect |
| 124. #343 | D17 | semidirect |
| 152. C17 | #1882 | semidirect |
| 177. M16 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587595 | 2 |
| #11763290 | 2 |
| C2×#10587496 | 2 |
| #11762819 | 2 |
| #11762714 | 2 |
| #11762570 | 2 |
| C17×#343 | 2 |
| #1882 | 17 |