Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
286 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11762851 | C2 | semidirect |
| 4. #11762675 | C2 | semidirect |
| 5. #11762577 | C2 | semidirect |
| 6. #11762569 | C2 | semidirect |
| 20. C17×#104 | C4 | semidirect |
| 40. M16×C17 | C2×C4 | semidirect |
| 43. C42×C17 | C2×C4 | semidirect |
| 133. #104 | Dic17 | semidirect |
| 137. C17 | #1860 | semidirect |
| 154. M16 | C2×Dic17 | semidirect |
| 169. C42 | C2×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763292 | 2 |
| #11762851 | 2 |
| #11762810 | 2 |
| #11762675 | 2 |
| #11762577 | 2 |
| #11762569 | 2 |
| C2×C17×#104 | 2 |
| #1860 | 17 |