Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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. #11763679 | C2 | semidirect |
| 9. C2×C4⋊C4×C17 | C4 | semidirect |
| 11. C2×C4⋊Dic17 | C4 | semidirect |
| 15. #10587578 | C4 | semidirect |
| 103. C2×C4⋊C4 | #595 | semidirect |
| 111. C17 | #1826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763780 | 2 |
| C4×C22⋊#595 | 2 |
| #11763679 | 2 |
| C2×#10587578 | 2 |
| #1826 | 17 |