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×#16864653 | C2 | semidirect |
| 2. C22×#16864642 | C2 | semidirect |
| 3. C2×#22576131 | C2 | semidirect |
| 4. #31774039 | C2 | direct (N × H) |
| 5. C2×#22576085 | C2 | semidirect |
| 6. C2×#22576081 | C2 | semidirect |
| 7. C2×(C2×D271)⋊C8 | C2 | semidirect |
| 8. C22×D8×C271 | C2 | semidirect |
| 12. C2×#16864653 | C22 | semidirect |
| 19. C2×#16864642 | C22 | semidirect |
| 22. #22576131 | C22 | semidirect |
| 25. #22576085 | C22 | semidirect |
| 26. #22576081 | C22 | semidirect |
| 27. (C2×D271)⋊C8 | C22 | semidirect |
| 31. C2×D8×C271 | C22 | semidirect |
| 39. C2×Dic542 | D4 | semidirect |
| 67. C2×D4×C271 | D4 | semidirect |
| 80. Dic542 | C2×D4 | semidirect |
| 108. D4×C271 | C2×D4 | semidirect |
| 138. C2×C271 | #449 | semidirect |
| 143. C271 | C2×#449 | semidirect |
| 147. C22×D8 | D271 | semidirect |
| 167. C2×D8 | C2×D271 | semidirect |
| 196. C2×D4 | C22⋊D271 | semidirect |
| 241. D4 | C2×C22⋊D271 | semidirect |
| 283. C2 | #31774039 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864653 | 2 |
| C22×#16864642 | 2 |
| C2×#22576131 | 2 |
| #31774039 | 2 |
| C2×#22576085 | 2 |
| C2×#22576081 | 2 |
| C2×(C2×D271)⋊C8 | 2 |
| C22×D8×C271 | 2 |
| C2×#449 | 271 |