Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
464 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. C2×#22576166 | C2 | semidirect |
| 3. #31774020 | C2 | direct (N × H) |
| 4. C2×#22576096 | C2 | semidirect |
| 5. C2×#22576088 | C2 | semidirect |
| 6. C2×#97×C271 | C2 | semidirect |
| 8. #22576182 | C4 | semidirect |
| 10. C2×Dic1084 | C4 | semidirect |
| 11. C2×#16864643 | C4 | semidirect |
| 12. C2×D2168 | C4 | semidirect |
| 14. #22576166 | C22 | semidirect |
| 18. #22576096 | C22 | semidirect |
| 19. #22576088 | C22 | semidirect |
| 23. #97×C271 | C22 | semidirect |
| 32. Dic1084 | C2×C4 | semidirect |
| 33. #16864643 | C2×C4 | semidirect |
| 34. D2168 | C2×C4 | semidirect |
| 88. C2×C271 | #444 | semidirect |
| 91. C271 | C2×#444 | semidirect |
| 98. C2×#97 | D271 | semidirect |
| 115. #97 | C2×D271 | semidirect |
| 181. C2 | #31774020 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576182 | 2 |
| C2×#22576166 | 2 |
| #31774020 | 2 |
| C2×#22576096 | 2 |
| C2×#22576088 | 2 |
| C2×#97×C271 | 2 |
| C2×#444 | 271 |