Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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. #41×Dic17 | C2 | semidirect |
| 3. C2×#10587496 | C2 | semidirect |
| 4. #11762782 | C2 | semidirect |
| 5. #11762580 | C2 | semidirect |
| 6. #11762568 | C2 | semidirect |
| 7. C17×#421 | C2 | semidirect |
| 12. #10587637 | C4 | semidirect |
| 14. #10587635 | C4 | semidirect |
| 45. C2×D68 | C2×C4 | semidirect |
| 47. C2×Dic34 | C2×C4 | semidirect |
| 68. #63223 | C2×C4 | semidirect |
| 126. #421 | D17 | semidirect |
| 158. C17 | #1906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763607 | 2 |
| #41×Dic17 | 2 |
| C2×#10587496 | 2 |
| #11762782 | 2 |
| #11762580 | 2 |
| #11762568 | 2 |
| C17×#421 | 2 |
| #1906 | 17 |