Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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. #11763575 | C2 | semidirect |
| 3. #11762793 | C2 | semidirect |
| 4. #11762792 | C2 | semidirect |
| 5. C2×#10587494 | C2 | semidirect |
| 6. #100×D17 | C2 | semidirect |
| 7. C17×#413 | C2 | semidirect |
| 18. C2×M16×C17 | C22 | semidirect |
| 19. C2×#63223 | C22 | semidirect |
| 21. M16×D17 | C22 | semidirect |
| 23. C17×#101 | C22 | semidirect |
| 24. C17×#100 | C22 | semidirect |
| 25. #10587507 | C22 | semidirect |
| 26. #10587504 | C22 | semidirect |
| 27. #10587494 | C22 | semidirect |
| 119. #413 | D17 | semidirect |
| 142. C2×M16 | C2×D17 | semidirect |
| 144. #101 | C2×D17 | semidirect |
| 147. #100 | C2×D17 | semidirect |
| 148. C17 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587696 | 2 |
| #11763575 | 2 |
| #11762793 | 2 |
| #11762792 | 2 |
| C2×#10587494 | 2 |
| #100×D17 | 2 |
| C17×#413 | 2 |
| #2888 | 17 |