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×#22576184 | C2 | semidirect |
| 3. #31774407 | C2 | semidirect |
| 4. #31774050 | C2 | semidirect |
| 5. #31774049 | C2 | semidirect |
| 6. #31774048 | C2 | semidirect |
| 7. #31774030 | C2 | semidirect |
| 8. #31774029 | C2 | semidirect |
| 9. #31773900 | C2 | semidirect |
| 10. #31773859 | C2 | semidirect |
| 11. #447×C271 | C2 | semidirect |
| 13. C2×#16864653 | C22 | semidirect |
| 23. C2×#16864643 | C22 | semidirect |
| 24. C2×#16864642 | C22 | semidirect |
| 25. C2×#16864639 | C22 | semidirect |
| 26. C2×#16864637 | C22 | semidirect |
| 28. #22576140 | C22 | semidirect |
| 29. #22576139 | C22 | semidirect |
| 30. #22576131 | 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×D8×C271 | C22 | semidirect |
| 42. #121×C271 | C22 | semidirect |
| 43. #102×C271 | C22 | semidirect |
| 44. C22⋊C8×C271 | C22 | semidirect |
| 53. C2×Dic542 | C23 | semidirect |
| 67. D4×D271 | D4 | semidirect |
| 79. C2×C271⋊C8 | C23 | semidirect |
| 81. C4⋊Dic271 | C23 | semidirect |
| 93. C2×D4×C271 | C23 | semidirect |
| 96. C2×C8×C271 | C23 | semidirect |
| 97. C4⋊C4×C271 | C23 | semidirect |
| 159. C22×C271 | AGL(1,ℤ/8) | semidirect |
| 173. C2×D271 | AGL(1,ℤ/8) | semidirect |
| 190. C271 | #3003 | semidirect |
| 200. #447 | D271 | semidirect |
| 218. C2×D8 | C2×D271 | semidirect |
| 224. #121 | C2×D271 | semidirect |
| 232. #102 | C2×D271 | semidirect |
| 235. C22⋊C8 | C2×D271 | semidirect |
| 264. C2×D4 | C22×D271 | semidirect |
| 279. C2×C8 | C22×D271 | semidirect |
| 283. C4⋊C4 | C22×D271 | semidirect |
| 363. C22 | #22576184 | 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×#22576184 | 2 |
| #31774407 | 2 |
| #31774050 | 2 |
| #31774049 | 2 |
| #31774048 | 2 |
| #31774030 | 2 |
| #31774029 | 2 |
| #31773900 | 2 |
| #31773859 | 2 |
| #447×C271 | 2 |
| #3003 | 271 |