Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16864641 | C2 | semidirect |
| 3. #31774375 | C2 | semidirect |
| 4. #31774121 | C2 | semidirect |
| 5. #31774095 | C2 | semidirect |
| 6. #31773925 | C2 | semidirect |
| 7. #31773903 | C2 | semidirect |
| 8. #31773893 | C2 | semidirect |
| 9. C2×#137×C271 | C2 | semidirect |
| 19. Q8×Dic271 | C22 | semidirect |
| 23. Dic271⋊C8 | C22 | semidirect |
| 24. #22576084 | C22 | semidirect |
| 26. #22576081 | C22 | semidirect |
| 30. C2×Q16×C271 | C22 | semidirect |
| 31. C2×SD16×C271 | C22 | semidirect |
| 55. C2×Q8×C271 | D4 | semidirect |
| 116. C271 | #3043 | semidirect |
| 118. C2×#137 | D271 | semidirect |
| 131. C2×Q16 | C2×D271 | semidirect |
| 134. C2×SD16 | C2×D271 | semidirect |
| 155. C2×Q8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864641 | 2 |
| #31774461 | 2 |
| #31774375 | 2 |
| #31774121 | 2 |
| #31774095 | 2 |
| #31773925 | 2 |
| #31773903 | 2 |
| #31773893 | 2 |
| C2×#137×C271 | 2 |
| #3043 | 271 |