Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1036 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
| 4. #11762722 | C2 | direct (N × H) |
| 5. C2×#10587502 | C2 | semidirect |
| 6. C2×C17×#95 | C2 | semidirect |
| 14. C22×Dic34 | C22 | semidirect |
| 19. C17×#95 | C22 | semidirect |
| 20. #10587502 | C22 | semidirect |
| 26. C23×D17 | Q8 | semidirect |
| 62. C22×D17 | C2×Q8 | semidirect |
| 104. C2×#95 | D17 | semidirect |
| 105. C2×C17 | #393 | semidirect |
| 125. #95 | C2×D17 | semidirect |
| 126. C17 | C2×#393 | semidirect |
| 205. C2 | #11762722 | 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 |
| C22×#63227 | 2 |
| #11762722 | 2 |
| C2×#10587502 | 2 |
| C2×C17×#95 | 2 |
| C2×#393 | 17 |