Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. C2×#10587481 | C2 | semidirect |
| 5. #11762714 | C2 | semidirect |
| 6. #11762563 | C2 | semidirect |
| 7. C17×#340 | C2 | semidirect |
| 19. C2×#63219 | C4 | semidirect |
| 47. C2×Dic34 | C2×C4 | semidirect |
| 50. C2×C8×C17 | C2×C4 | semidirect |
| 90. C2×Dic17 | SD16 | semidirect |
| 131. #340 | D17 | semidirect |
| 159. C17 | #1877 | semidirect |
| 188. C2×C8 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63219 | 2 |
| C2×#10587579 | 2 |
| C2×#10587481 | 2 |
| C2×#10587480 | 2 |
| #11762714 | 2 |
| #11762563 | 2 |
| C17×#340 | 2 |
| #1877 | 17 |