Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
994 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 143 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×D4×D271 | C2 | semidirect |
| 2. C2×#22576187 | C2 | semidirect |
| 3. #31774410 | C2 | semidirect |
| 4. #31774047 | C2 | semidirect |
| 5. #31774046 | C2 | semidirect |
| 6. #31774033 | C2 | semidirect |
| 7. #31774032 | C2 | semidirect |
| 8. #31774031 | C2 | semidirect |
| 9. #31773900 | C2 | semidirect |
| 10. #31773859 | C2 | semidirect |
| 11. #450×C271 | C2 | semidirect |
| 13. C2×#16864655 | C22 | semidirect |
| 23. C2×#16864641 | C22 | semidirect |
| 24. C2×D2168 | C22 | semidirect |
| 25. C2×#16864639 | C22 | semidirect |
| 26. C2×#16864637 | C22 | semidirect |
| 28. #22576136 | C22 | semidirect |
| 29. #22576135 | C22 | semidirect |
| 30. #22576134 | C22 | semidirect |
| 34. #22576118 | C22 | semidirect |
| 35. #22576082 | C22 | semidirect |
| 36. #22576081 | C22 | semidirect |
| 37. #22576080 | C22 | semidirect |
| 38. C22⋊(C271⋊C8) | C22 | semidirect |
| 39. (C2×D271)⋊C8 | C22 | semidirect |
| 41. C2×SD16×C271 | C22 | semidirect |
| 42. C22⋊Q8×C271 | C22 | semidirect |
| 43. #102×C271 | C22 | semidirect |
| 44. C22⋊C8×C271 | C22 | semidirect |
| 58. C2×D1084 | C23 | semidirect |
| 68. D4×D271 | D4 | semidirect |
| 80. C2×C271⋊C8 | C23 | semidirect |
| 81. C4⋊Dic271 | C23 | semidirect |
| 89. C2×Q8×C271 | C23 | semidirect |
| 95. C2×C8×C271 | C23 | semidirect |
| 97. C4⋊C4×C271 | C23 | semidirect |
| 156. C22×C271 | AGL(1,ℤ/8) | semidirect |
| 173. C2×D271 | AGL(1,ℤ/8) | semidirect |
| 190. C271 | #3003 | semidirect |
| 197. #450 | D271 | semidirect |
| 216. C2×SD16 | C2×D271 | semidirect |
| 222. C22⋊Q8 | C2×D271 | semidirect |
| 232. #102 | C2×D271 | semidirect |
| 235. C22⋊C8 | C2×D271 | semidirect |
| 245. C2×Q8 | C22×D271 | semidirect |
| 279. C2×C8 | C22×D271 | semidirect |
| 283. C4⋊C4 | C22×D271 | semidirect |
| 363. C22 | #22576187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D271 | 2 |
| C2×#22576187 | 2 |
| #31774410 | 2 |
| #31774047 | 2 |
| #31774046 | 2 |
| #31774033 | 2 |
| #31774032 | 2 |
| #31774031 | 2 |
| #31773900 | 2 |
| #31773859 | 2 |
| #450×C271 | 2 |
| #3003 | 271 |