Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1968 conjugacy classes of subgroups; only the 605 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 605 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 |
|---|---|---|
| 2. C23×C4×D17 | C2 | semidirect |
| 3. C2×#10587569 | C2 | direct (N × H) |
| 4. C22×C4⋊Dic17 | C2 | semidirect |
| 5. C22×#63225 | C2 | semidirect |
| 6. C22×C22⋊Dic17 | C2 | semidirect |
| 7. C22×#63227 | C2 | semidirect |
| 8. C22×C22⋊C4×C17 | C2 | semidirect |
| 19. C22×C4×D17 | C22 | semidirect |
| 20. C2×C22⋊C4×C17 | C22 | semidirect |
| 21. C2×C22⋊Dic17 | C22 | semidirect |
| 22. C2×#63227 | C22 | semidirect |
| 23. C2×C4⋊Dic17 | C22 | semidirect |
| 24. C2×#63225 | C22 | semidirect |
| 25. #10587569 | C22 | direct (N × H) |
| 48. C2×C4×D17 | C23 | semidirect |
| 49. C22⋊C4×C17 | C23 | semidirect |
| 50. C22⋊Dic17 | C23 | semidirect |
| 51. #63227 | C23 | semidirect |
| 52. C4⋊Dic17 | C23 | semidirect |
| 53. #63225 | C23 | semidirect |
| 85. C22×C17 | #123 | semidirect |
| 106. C22×C22⋊C4 | D17 | semidirect |
| 108. C2×C17 | C2×#123 | semidirect |
| 129. C2×C22⋊C4 | C2×D17 | semidirect |
| 130. C17 | C22×#123 | semidirect |
| 158. C22⋊C4 | C22×D17 | semidirect |
| 193. C22 | #10587569 | direct (N × H) |
| 205. C2 | C2×#10587569 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D17 | 2 |
| C23×C4×D17 | 2 |
| C2×#10587569 | 2 |
| C22×C4⋊Dic17 | 2 |
| C22×#63225 | 2 |
| C22×C22⋊Dic17 | 2 |
| C22×#63227 | 2 |
| C22×C22⋊C4×C17 | 2 |
| C22×#123 | 17 |