Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#16864655 | C2 | semidirect |
| 2. C22×#16864639 | C2 | semidirect |
| 3. C2×#22576131 | C2 | semidirect |
| 4. #31774041 | C2 | direct (N × H) |
| 5. C2×#22576084 | C2 | semidirect |
| 6. C2×#22576082 | C2 | semidirect |
| 7. C2×(C2×D271)⋊C8 | C2 | semidirect |
| 8. C22×SD16×C271 | C2 | semidirect |
| 12. C2×#16864655 | C22 | semidirect |
| 19. C2×#16864639 | C22 | semidirect |
| 22. #22576131 | C22 | semidirect |
| 25. #22576084 | C22 | semidirect |
| 26. #22576082 | C22 | semidirect |
| 27. (C2×D271)⋊C8 | C22 | semidirect |
| 31. C2×SD16×C271 | C22 | semidirect |
| 42. C2×D1084 | D4 | semidirect |
| 63. C2×Q8×C271 | D4 | semidirect |
| 85. D1084 | C2×D4 | semidirect |
| 103. Q8×C271 | C2×D4 | semidirect |
| 137. C2×C271 | #449 | semidirect |
| 143. C271 | C2×#449 | semidirect |
| 146. C22×SD16 | D271 | semidirect |
| 165. C2×SD16 | C2×D271 | semidirect |
| 185. C2×Q8 | C22⋊D271 | semidirect |
| 233. Q8 | C2×C22⋊D271 | semidirect |
| 283. C2 | #31774041 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864655 | 2 |
| C22×#16864639 | 2 |
| C2×#22576131 | 2 |
| #31774041 | 2 |
| C2×#22576084 | 2 |
| C2×#22576082 | 2 |
| C2×(C2×D271)⋊C8 | 2 |
| C22×SD16×C271 | 2 |
| C2×#449 | 271 |