Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
412 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 117 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. C4×C22⋊Dic17 | C2 | semidirect |
| 4. #11762575 | C2 | semidirect |
| 5. C4×C22⋊C4×C17 | C2 | semidirect |
| 8. C22×C4×D17 | C4 | semidirect |
| 17. C2×#63227 | C4 | semidirect |
| 18. C2×#63225 | C4 | semidirect |
| 20. C2×C4×Dic17 | C4 | semidirect |
| 23. #10587477 | C4 | direct (N × H) |
| 46. C22⋊C4×C17 | C2×C4 | semidirect |
| 51. C22⋊Dic17 | C2×C4 | semidirect |
| 70. C22×D17 | C42 | semidirect |
| 95. C2×Dic17 | C42 | semidirect |
| 121. C4×C17 | #99 | semidirect |
| 129. C4×C22⋊C4 | D17 | semidirect |
| 157. C17 | C4×#99 | semidirect |
| 188. C22⋊C4 | C4×D17 | semidirect |
| 258. C4 | #10587477 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D17 | 2 |
| C2×#10587477 | 2 |
| C4×C22⋊Dic17 | 2 |
| #11762575 | 2 |
| C4×C22⋊C4×C17 | 2 |
| C4×#99 | 17 |