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×#22576186 | C2 | semidirect |
| 3. C2×#22576182 | C2 | semidirect |
| 4. #31774471 | C2 | semidirect |
| 5. #31774464 | C2 | semidirect |
| 6. #31774288 | C2 | semidirect |
| 7. #31774283 | C2 | semidirect |
| 8. #31774278 | C2 | semidirect |
| 9. #31774268 | C2 | semidirect |
| 10. #31773852 | C2 | semidirect |
| 11. C22×SD16×C271 | C2 | semidirect |
| 17. C2×Dic1084 | C22 | semidirect |
| 18. C2×#16864644 | C22 | semidirect |
| 19. C2×#16864643 | C22 | semidirect |
| 20. C2×#16864643 | C22 | semidirect |
| 22. C2×#16864641 | C22 | semidirect |
| 23. C2×D2168 | C22 | semidirect |
| 26. #22576158 | C22 | semidirect |
| 28. #22576149 | C22 | semidirect |
| 35. #22576070 | C22 | semidirect |
| 36. C8×Dic271 | C22 | semidirect |
| 64. #16864638 | D4 | semidirect |
| 85. C2×C8×C271 | D4 | semidirect |
| 148. C271 | #3154 | semidirect |
| 153. C22×SD16 | D271 | semidirect |
| 228. C2×C8 | C22⋊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×#22576186 | 2 |
| C2×#22576182 | 2 |
| #31774471 | 2 |
| #31774464 | 2 |
| #31774288 | 2 |
| #31774283 | 2 |
| #31774278 | 2 |
| #31774268 | 2 |
| #31773852 | 2 |
| C22×SD16×C271 | 2 |
| #3154 | 271 |