Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
332 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 332 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 |
|---|---|---|
| 2. C2×#10587587 | C2 | semidirect |
| 3. #11762811 | C2 | semidirect |
| 4. C2×#10587492 | C2 | semidirect |
| 5. C2×#10587494 | C2 | semidirect |
| 6. #11762577 | C2 | semidirect |
| 7. C17×#341 | C2 | semidirect |
| 16. #10587594 | C4 | semidirect |
| 123. #341 | D17 | semidirect |
| 151. C17 | #1907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587594 | 2 |
| C2×#10587587 | 2 |
| #11762811 | 2 |
| C2×#10587492 | 2 |
| C2×#10587494 | 2 |
| #11762577 | 2 |
| C17×#341 | 2 |
| #1907 | 17 |