Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C4×Dic17 | C2 | semidirect |
| 3. C2×#10587496 | C2 | direct (N × H) |
| 4. C22×M16×C17 | C2 | semidirect |
| 10. C2×#63252 | C4 | semidirect |
| 12. C22×D68 | C4 | semidirect |
| 14. C22×Dic34 | C4 | semidirect |
| 16. C2×M16×C17 | C22 | semidirect |
| 19. C2×C4×Dic17 | C22 | semidirect |
| 20. #10587496 | C22 | direct (N × H) |
| 37. #63252 | C2×C4 | semidirect |
| 40. C2×D68 | C2×C4 | semidirect |
| 44. C2×Dic34 | C2×C4 | semidirect |
| 46. M16×C17 | C23 | semidirect |
| 49. C4×Dic17 | C23 | semidirect |
| 71. D68 | C22×C4 | semidirect |
| 75. Dic34 | C22×C4 | semidirect |
| 80. C22×C17 | #104 | semidirect |
| 93. C22×M16 | D17 | semidirect |
| 98. C2×C17 | C2×#104 | semidirect |
| 112. C2×M16 | C2×D17 | semidirect |
| 117. C17 | C22×#104 | semidirect |
| 143. M16 | C22×D17 | semidirect |
| 178. C22 | #10587496 | direct (N × H) |
| 191. C2 | C2×#10587496 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63252 | 2 |
| C22×C4×Dic17 | 2 |
| C2×#10587496 | 2 |
| C22×M16×C17 | 2 |
| C22×#104 | 17 |