Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
338 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 18. C2×Q16×C17 | C4 | semidirect |
| 19. C2×#63231 | C4 | semidirect |
| 20. C2×#63231 | C4 | semidirect |
| 23. C2×Dic68 | C4 | semidirect |
| 81. C2×#595 | Q16 | semidirect |
| 152. C2×Q16 | #595 | semidirect |
| 166. C17 | #1878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#595 | 2 |
| C2×#10587549 | 2 |
| (C2×#595)⋊Q8 | 2 |
| #11763683 | 2 |
| #11763674 | 2 |
| C2×Q16×D17 | 2 |
| #1878 | 17 |