Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#10587476 | C2 | semidirect |
| 3. #11762811 | C2 | semidirect |
| 4. #11762810 | C2 | semidirect |
| 5. #11762675 | C2 | semidirect |
| 6. #11762577 | C2 | semidirect |
| 7. C2×C17×#104 | C2 | semidirect |
| 52. C42×C17 | D4 | semidirect |
| 123. C2×#104 | D17 | semidirect |
| 154. C17 | #2040 | semidirect |
| 190. C42 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763387 | 2 |
| C2×#10587476 | 2 |
| #11762811 | 2 |
| #11762810 | 2 |
| #11762675 | 2 |
| #11762577 | 2 |
| C2×C17×#104 | 2 |
| #2040 | 17 |