Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1840 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 725 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 |
|---|---|---|
| 1. C23×Dic34 | C2 | semidirect |
| 2. C2×#10587610 | C2 | direct (N × H) |
| 3. C22×C4⋊Dic17 | C2 | semidirect |
| 4. C22×#63225 | C2 | semidirect |
| 15. C22×Dic34 | C22 | semidirect |
| 17. C2×C4⋊Dic17 | C22 | semidirect |
| 18. #10587610 | C22 | direct (N × H) |
| 19. C2×#63225 | C22 | semidirect |
| 22. C24×C17 | Q8 | semidirect |
| 36. C2×Dic34 | C23 | semidirect |
| 38. C4⋊Dic17 | C23 | semidirect |
| 39. #63225 | C23 | semidirect |
| 45. C23×C17 | C2×Q8 | semidirect |
| 63. C22×C17 | C22⋊Q8 | semidirect |
| 66. C22×C17 | C22×Q8 | semidirect |
| 80. C2×C17 | C2×C22⋊Q8 | semidirect |
| 97. C17 | C22×C22⋊Q8 | semidirect |
| 100. C24 | Dic34 | semidirect |
| 122. C23 | C2×Dic34 | semidirect |
| 140. C22 | #10587610 | direct (N × H) |
| 142. C22 | C22×Dic34 | semidirect |
| 151. C2 | C2×#10587610 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic34 | 2 |
| C2×#10587610 | 2 |
| C22×C4⋊Dic17 | 2 |
| C22×#63225 | 2 |
| C22×C22⋊Dic17 | 2 |
| C24×C4×C17 | 2 |
| C22×C22⋊Q8 | 17 |