Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
996 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×SD16×D271 | C2 | semidirect |
| 3. C22⋊Q8×D271 | C2 | semidirect |
| 4. #31774050 | C2 | semidirect |
| 5. #31774049 | C2 | semidirect |
| 6. #31774048 | C2 | semidirect |
| 7. #31774047 | C2 | semidirect |
| 8. #31774046 | C2 | semidirect |
| 9. #102×D271 | C2 | semidirect |
| 10. C22⋊C8×D271 | C2 | semidirect |
| 11. #450×C271 | C2 | semidirect |
| 13. C2×Q8×D271 | C22 | semidirect |
| 22. C2×#16864643 | C22 | semidirect |
| 23. C2×#16864642 | C22 | semidirect |
| 24. C2×#16864641 | C22 | semidirect |
| 26. C2×C8×D271 | C22 | semidirect |
| 27. #22576140 | C22 | semidirect |
| 28. #22576139 | C22 | semidirect |
| 31. #22576136 | C22 | semidirect |
| 33. C4⋊C4×D271 | 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 |
| 53. C2×Dic542 | C23 | semidirect |
| 78. 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 |
| 112. C22×D271 | SD16 | semidirect |
| 155. C22×C271 | C2×SD16 | semidirect |
| 168. C2×D271 | C2×SD16 | semidirect |
| 185. D271 | #450 | direct (N × H) |
| 186. C271 | C2×#450 | semidirect |
| 196. #450 | D271 | direct (N × H) |
| 214. C2×SD16 | C2×D271 | semidirect |
| 221. C22⋊Q8 | C2×D271 | semidirect |
| 228. #102 | C2×D271 | semidirect |
| 231. C22⋊C8 | C2×D271 | semidirect |
| 243. C2×Q8 | C22×D271 | semidirect |
| 274. C2×C8 | C22×D271 | semidirect |
| 281. C4⋊C4 | C22×D271 | semidirect |
| 355. C22 | SD16×D271 | 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×SD16×D271 | 2 |
| C22⋊Q8×D271 | 2 |
| #31774050 | 2 |
| #31774049 | 2 |
| #31774048 | 2 |
| #31774047 | 2 |
| #31774046 | 2 |
| #102×D271 | 2 |
| C22⋊C8×D271 | 2 |
| #450×C271 | 2 |
| C2×#450 | 271 |