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. #31774550 | C2 | semidirect |
| 2. #31774532 | C2 | semidirect |
| 3. #31774209 | C2 | semidirect |
| 4. #31774174 | C2 | semidirect |
| 5. #31774132 | C2 | semidirect |
| 6. #31774089 | C2 | semidirect |
| 7. #31774032 | C2 | semidirect |
| 8. C4×D2168 | C2 | semidirect |
| 9. C8×D1084 | C2 | semidirect |
| 10. #102×D271 | C2 | semidirect |
| 11. #486×C271 | C2 | semidirect |
| 16. C2×#16864639 | C22 | semidirect |
| 17. C2×C8×D271 | C22 | semidirect |
| 20. #22576135 | C22 | semidirect |
| 26. C4×D1084 | C22 | semidirect |
| 27. C4⋊C4×D271 | C22 | semidirect |
| 28. #22576094 | C22 | semidirect |
| 29. #22576093 | C22 | semidirect |
| 30. C4⋊(C271⋊C8) | C22 | semidirect |
| 32. #22576082 | C22 | semidirect |
| 33. #22576081 | C22 | semidirect |
| 35. (C2×D271)⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C271 | C22 | semidirect |
| 38. #102×C271 | C22 | semidirect |
| 39. #102×C271 | C22 | semidirect |
| 40. C4×C8×C271 | C22 | semidirect |
| 88. D1084 | D8 | semidirect |
| 89. D1084 | #41 | semidirect |
| 142. C271 | #3294 | semidirect |
| 146. #486 | D271 | semidirect |
| 161. C4⋊Q8 | C2×D271 | semidirect |
| 180. #102 | C2×D271 | semidirect |
| 181. #102 | C2×D271 | semidirect |
| 183. C4×C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774550 | 2 |
| #31774532 | 2 |
| #31774209 | 2 |
| #31774174 | 2 |
| #31774132 | 2 |
| #31774089 | 2 |
| #31774032 | 2 |
| C4×D2168 | 2 |
| C8×D1084 | 2 |
| #102×D271 | 2 |
| #486×C271 | 2 |
| #3294 | 271 |