Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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. C4×Dic68 | C2 | semidirect |
| 4. #11762635 | C2 | semidirect |
| 5. #11762614 | C2 | semidirect |
| 7. C17×#346 | C2 | semidirect |
| 19. #10587471 | C4 | semidirect |
| 32. Dic68 | C2×C4 | semidirect |
| 36. C16×C17 | C2×C4 | semidirect |
| 70. #346 | D17 | semidirect |
| 87. C17 | #2175 | semidirect |
| 104. C16 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587471 | 2 |
| C4×Dic68 | 2 |
| C4×D136 | 2 |
| #11762635 | 2 |
| #11762614 | 2 |
| #11762611 | 2 |
| C17×#346 | 2 |
| #2175 | 17 |