Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#22576186 | C2 | semidirect |
| 2. #31774568 | C2 | semidirect |
| 3. #31774273 | C2 | semidirect |
| 4. #31774148 | C2 | semidirect |
| 5. #31774094 | C2 | semidirect |
| 6. #31774092 | C2 | semidirect |
| 7. #31774040 | C2 | semidirect |
| 8. #31774031 | C2 | semidirect |
| 9. C4×#16864642 | C2 | semidirect |
| 10. #31773975 | C2 | semidirect |
| 11. D42×C271 | C2 | semidirect |
| 12. C2×#16864654 | C22 | semidirect |
| 15. C2×#16864642 | C22 | semidirect |
| 17. C2×#16864639 | C22 | semidirect |
| 18. C2×#16864639 | C22 | semidirect |
| 19. C2×#16864638 | C22 | semidirect |
| 20. #22576157 | C22 | semidirect |
| 22. #22576134 | C22 | semidirect |
| 24. C4×Dic542 | C22 | semidirect |
| 26. #22576091 | C22 | semidirect |
| 27. C4⋊(C271⋊C8) | C22 | semidirect |
| 28. #22576083 | C22 | semidirect |
| 30. #22576081 | C22 | semidirect |
| 31. #22576080 | C22 | semidirect |
| 32. C22⋊(C271⋊C8) | C22 | semidirect |
| 33. C4×C271⋊C8 | C22 | semidirect |
| 52. #16864642 | D4 | semidirect |
| 85. Dic542 | C2×D4 | semidirect |
| 97. C271⋊C8 | C2×D4 | semidirect |
| 138. C4×C271 | AGL(1,ℤ/8) | semidirect |
| 150. C271 | #3274 | semidirect |
| 154. D42 | D271 | semidirect |
| 291. C4 | #22576186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576186 | 2 |
| #31774568 | 2 |
| #31774273 | 2 |
| #31774148 | 2 |
| #31774094 | 2 |
| #31774092 | 2 |
| #31774040 | 2 |
| #31774031 | 2 |
| C4×#16864642 | 2 |
| #31773975 | 2 |
| D42×C271 | 2 |
| #3274 | 271 |