Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 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. #11763700 | C2 | semidirect |
| 4. #11763699 | C2 | semidirect |
| 9. #10587538 | C4 | semidirect |
| 15. #10587529 | C4 | semidirect |
| 16. C17×M32 | C4 | semidirect |
| 17. #10587483 | C4 | semidirect |
| 19. C16×D17 | C4 | semidirect |
| 35. #63216 | C2×C4 | semidirect |
| 36. C16×C17 | C2×C4 | semidirect |
| 37. #63214 | C2×C4 | semidirect |
| 73. D17 | #347 | semidirect |
| 81. M32 | #595 | semidirect |
| 88. C17 | C2×#347 | semidirect |
| 106. C16 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763865 | 2 |
| C2×#10587532 | 2 |
| #11763700 | 2 |
| #11763699 | 2 |
| M32×D17 | 2 |
| C2×#347 | 17 |