Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#10587477 | C2 | semidirect |
| 3. #11762669 | C2 | semidirect |
| 4. C4×C22⋊C4×C17 | C2 | semidirect |
| 7. C22×D68 | C4 | semidirect |
| 15. C2×#63227 | C4 | semidirect |
| 17. C2×C4⋊Dic17 | C4 | semidirect |
| 41. C22⋊C4×C17 | D4 | semidirect |
| 105. C4×C17 | #99 | semidirect |
| 111. C4×C22⋊C4 | D17 | semidirect |
| 136. C17 | #1964 | semidirect |
| 163. C22⋊C4 | D68 | semidirect |
| 222. C4 | #10587477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587616 | 2 |
| C2×#10587477 | 2 |
| #11762669 | 2 |
| C4×C22⋊C4×C17 | 2 |
| #1964 | 17 |