Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#16864641 | C2 | semidirect |
| 2. C2×#22576167 | C2 | semidirect |
| 4. #31774145 | C2 | semidirect |
| 5. #31774128 | C2 | semidirect |
| 6. #31773933 | C2 | semidirect |
| 7. #31773906 | C2 | semidirect |
| 8. #31773901 | C2 | semidirect |
| 9. #536×C271 | C2 | semidirect |
| 16. C2×#16864638 | C22 | semidirect |
| 18. C22×C271⋊C8 | C22 | semidirect |
| 24. #22576093 | C22 | semidirect |
| 25. #22576091 | C22 | semidirect |
| 26. #22576084 | C22 | semidirect |
| 33. C22⋊Q8×C271 | C22 | semidirect |
| 46. C2×C271⋊C8 | D4 | semidirect |
| 120. C271 | #3057 | semidirect |
| 124. #536 | D271 | semidirect |
| 147. C22⋊Q8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864641 | 2 |
| C2×#22576167 | 2 |
| #31774461 | 2 |
| #31774145 | 2 |
| #31774128 | 2 |
| #31773933 | 2 |
| #31773906 | 2 |
| #31773901 | 2 |
| #536×C271 | 2 |
| #3057 | 271 |