Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #31774445 | C2 | semidirect |
| 2. C4×D4×D271 | C2 | semidirect |
| 3. #31774209 | C2 | semidirect |
| 4. #31774178 | C2 | semidirect |
| 5. #31774177 | C2 | semidirect |
| 6. #31774089 | C2 | semidirect |
| 7. #31774029 | C2 | semidirect |
| 8. D8×Dic271 | C2 | semidirect |
| 9. #31773977 | C2 | semidirect |
| 10. #31773949 | C2 | semidirect |
| 11. #459×C271 | C2 | semidirect |
| 16. #22576160 | C22 | semidirect |
| 23. D4×Dic271 | C22 | semidirect |
| 30. #22576094 | C22 | semidirect |
| 31. #22576093 | C22 | semidirect |
| 32. C4⋊(C271⋊C8) | C22 | semidirect |
| 35. #22576081 | C22 | semidirect |
| 37. C8×Dic271 | C22 | semidirect |
| 39. #127×C271 | C22 | semidirect |
| 41. C4⋊C8×C271 | C22 | semidirect |
| 42. #102×C271 | C22 | semidirect |
| 91. D1084 | #41 | semidirect |
| 107. C4×D271 | D8 | semidirect |
| 116. D4×C271 | #41 | semidirect |
| 154. C271 | #3100 | semidirect |
| 162. #459 | D271 | semidirect |
| 173. #127 | C2×D271 | semidirect |
| 191. C4⋊C8 | C2×D271 | semidirect |
| 195. #102 | C2×D271 | semidirect |
| 256. D4 | #16864653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774445 | 2 |
| C4×D4×D271 | 2 |
| #31774209 | 2 |
| #31774178 | 2 |
| #31774177 | 2 |
| #31774089 | 2 |
| #31774029 | 2 |
| D8×Dic271 | 2 |
| #31773977 | 2 |
| #31773949 | 2 |
| #459×C271 | 2 |
| #3100 | 271 |