Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22576191 | C2 | semidirect |
| 2. C2×#22576185 | C2 | semidirect |
| 3. C2×#22576180 | C2 | semidirect |
| 4. C22×#16864641 | C2 | semidirect |
| 5. #31774466 | C2 | semidirect |
| 6. #31774289 | C2 | semidirect |
| 7. #31774287 | C2 | semidirect |
| 8. #31774279 | C2 | semidirect |
| 9. #31774271 | C2 | semidirect |
| 10. #31773853 | C2 | semidirect |
| 11. #536×C271 | C2 | semidirect |
| 17. C2×#16864644 | C22 | semidirect |
| 18. C2×#16864644 | C22 | semidirect |
| 19. C2×#16864642 | C22 | semidirect |
| 24. C2×#16864641 | C22 | semidirect |
| 25. C2×#16864641 | C22 | semidirect |
| 27. C2×#16864639 | C22 | semidirect |
| 34. #22576071 | C22 | semidirect |
| 35. C4×C271⋊C8 | C22 | semidirect |
| 38. C4⋊Q8×C271 | C22 | semidirect |
| 39. #124×C271 | C22 | semidirect |
| 65. #16864638 | D4 | semidirect |
| 66. C2×C271⋊C8 | D4 | semidirect |
| 148. C271 | #3154 | semidirect |
| 154. #536 | D271 | semidirect |
| 181. C4⋊Q8 | C2×D271 | semidirect |
| 184. #124 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576191 | 2 |
| C2×#22576185 | 2 |
| C2×#22576180 | 2 |
| C22×#16864641 | 2 |
| #31774466 | 2 |
| #31774289 | 2 |
| #31774287 | 2 |
| #31774279 | 2 |
| #31774271 | 2 |
| #31773853 | 2 |
| #536×C271 | 2 |
| #3154 | 271 |