Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11763662 | C2 | direct (N × H) |
| 7. C22×Dic34 | C4 | semidirect |
| 9. C2×C4⋊C4×C17 | C4 | semidirect |
| 14. #10587583 | C4 | semidirect |
| 36. C2×Dic34 | C2×C4 | semidirect |
| 40. C4⋊C4×C17 | C2×C4 | semidirect |
| 98. C2×C17 | #328 | semidirect |
| 114. C2×C4⋊C4 | #595 | semidirect |
| 120. C17 | C2×#328 | semidirect |
| 143. C4⋊C4 | C2×#595 | semidirect |
| 197. C2 | #11763662 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587543 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| #11763662 | 2 |
| C2×#10587583 | 2 |
| C2×#328 | 17 |