Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C22×#63219 | C2 | semidirect |
| 2. C2×#10587610 | C2 | semidirect |
| 4. #11763055 | C2 | direct (N × H) |
| 5. C2×#10587489 | C2 | semidirect |
| 6. C2×#10587487 | C2 | semidirect |
| 7. C2×#10587492 | C2 | semidirect |
| 8. C22×M16×C17 | C2 | semidirect |
| 14. C2×M16×C17 | C22 | semidirect |
| 24. #10587610 | C22 | semidirect |
| 27. C2×#63219 | C22 | semidirect |
| 28. #10587492 | C22 | semidirect |
| 29. #10587489 | C22 | semidirect |
| 30. #10587487 | C22 | semidirect |
| 54. C2×C8×C17 | D4 | semidirect |
| 97. C8×C17 | C2×D4 | semidirect |
| 119. C22×M16 | D17 | semidirect |
| 127. C2×C17 | #468 | semidirect |
| 139. C2×M16 | C2×D17 | semidirect |
| 154. C17 | C2×#468 | semidirect |
| 179. C2×C8 | C22⋊D17 | semidirect |
| 221. C8 | C2×C22⋊D17 | semidirect |
| 243. C2 | #11763055 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63219 | 2 |
| C2×#10587610 | 2 |
| C2×#10587616 | 2 |
| #11763055 | 2 |
| C2×#10587489 | 2 |
| C2×#10587487 | 2 |
| C2×#10587492 | 2 |
| C22×M16×C17 | 2 |
| C2×#468 | 17 |