Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31774552 | C2 | semidirect |
| 2. #31774532 | C2 | semidirect |
| 3. #31774243 | C2 | semidirect |
| 4. #31774209 | C2 | semidirect |
| 5. #31774178 | C2 | semidirect |
| 6. #31774130 | C2 | semidirect |
| 7. #31774029 | C2 | semidirect |
| 8. C4×#16864639 | C2 | semidirect |
| 9. #31773962 | C2 | semidirect |
| 10. #102×D271 | C2 | semidirect |
| 11. #459×C271 | C2 | semidirect |
| 16. C2×C8×D271 | C22 | semidirect |
| 17. #22576160 | C22 | semidirect |
| 22. #22576131 | C22 | semidirect |
| 26. C4⋊C4×D271 | C22 | semidirect |
| 27. #22576094 | C22 | semidirect |
| 28. #22576093 | C22 | semidirect |
| 30. #22576081 | C22 | semidirect |
| 31. #22576081 | C22 | semidirect |
| 32. #22576081 | C22 | semidirect |
| 34. (C2×D271)⋊C8 | C22 | semidirect |
| 35. C4×C271⋊C8 | C22 | semidirect |
| 36. C2×D8×C271 | C22 | semidirect |
| 38. C4×D4×C271 | C22 | semidirect |
| 39. C4⋊C8×C271 | C22 | semidirect |
| 40. #102×C271 | C22 | semidirect |
| 85. D1084 | D8 | semidirect |
| 86. D1084 | #41 | semidirect |
| 142. C271 | #3294 | semidirect |
| 150. #459 | D271 | semidirect |
| 159. C2×D8 | C2×D271 | semidirect |
| 171. C4×D4 | C2×D271 | semidirect |
| 175. C4⋊C8 | C2×D271 | semidirect |
| 181. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774552 | 2 |
| #31774532 | 2 |
| #31774243 | 2 |
| #31774209 | 2 |
| #31774178 | 2 |
| #31774130 | 2 |
| #31774029 | 2 |
| C4×#16864639 | 2 |
| #31773962 | 2 |
| #102×D271 | 2 |
| #459×C271 | 2 |
| #3294 | 271 |