Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 2. C22×#16864641 | C2 | semidirect |
| 3. #31774371 | C2 | semidirect |
| 4. #31774109 | C2 | semidirect |
| 5. #31774099 | C2 | semidirect |
| 6. #31773924 | C2 | semidirect |
| 7. #31773906 | C2 | semidirect |
| 8. #31773893 | C2 | semidirect |
| 9. #536×C271 | C2 | semidirect |
| 22. C4⋊(C271⋊C8) | C22 | semidirect |
| 23. #22576084 | C22 | semidirect |
| 24. #22576084 | C22 | semidirect |
| 25. #22576081 | C22 | semidirect |
| 28. C4⋊Q8×C271 | C22 | semidirect |
| 29. #124×C271 | C22 | semidirect |
| 116. C271 | #3042 | semidirect |
| 120. #536 | D271 | semidirect |
| 137. C4⋊Q8 | C2×D271 | semidirect |
| 138. #124 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576185 | 2 |
| C22×#16864641 | 2 |
| #31774371 | 2 |
| #31774109 | 2 |
| #31774099 | 2 |
| #31773924 | 2 |
| #31773906 | 2 |
| #31773893 | 2 |
| #536×C271 | 2 |
| #3042 | 271 |