Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
304 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 10. C2×Q16×C17 | C4 | semidirect |
| 11. C2×#63231 | C4 | semidirect |
| 14. C2×Dic68 | C4 | semidirect |
| 96. C2×Q16 | #595 | semidirect |
| 105. C17 | #1971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587533 | 2 |
| C2×#10587549 | 2 |
| C2×#10587532 | 2 |
| (C2×#595)⋊Q8 | 2 |
| C2×Q16×D17 | 2 |
| #1971 | 17 |