Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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. C2×#22576191 | C2 | semidirect |
| 3. C4×#16864654 | C2 | semidirect |
| 4. #31774116 | C2 | semidirect |
| 5. #31774109 | C2 | semidirect |
| 6. #31773921 | C2 | semidirect |
| 7. #31773906 | C2 | semidirect |
| 8. #31773902 | C2 | semidirect |
| 9. C2×#124×C271 | C2 | semidirect |
| 13. C2×#16864644 | C22 | semidirect |
| 15. C2×#16864641 | C22 | semidirect |
| 19. C4×Dic542 | C22 | semidirect |
| 20. C4×D1084 | C22 | semidirect |
| 25. C4⋊(C271⋊C8) | C22 | semidirect |
| 26. #22576084 | C22 | semidirect |
| 125. C271 | #3040 | semidirect |
| 129. C2×#124 | 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 |
| C4×#16864654 | 2 |
| #31774116 | 2 |
| #31774109 | 2 |
| #31773921 | 2 |
| #31773906 | 2 |
| #31773902 | 2 |
| C2×#124×C271 | 2 |
| #3040 | 271 |