Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11762669 | C2 | semidirect |
| 3. #11762544 | C2 | semidirect |
| 4. C2×C17×C22⋊C8 | C2 | semidirect |
| 7. C22×D68 | C4 | semidirect |
| 12. #10587616 | C4 | semidirect |
| 16. C2×C4⋊Dic17 | C4 | semidirect |
| 18. C17×C22⋊C8 | C22 | semidirect |
| 19. #10587502 | C22 | semidirect |
| 103. C2×C22⋊C8 | D17 | semidirect |
| 127. C22⋊C8 | C2×D17 | semidirect |
| 129. C17 | #1519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587616 | 2 |
| #11762669 | 2 |
| #11762544 | 2 |
| C2×C17×C22⋊C8 | 2 |
| #1519 | 17 |