Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31774174 | C2 | semidirect |
| 3. #31774099 | C2 | semidirect |
| 4. #31773641 | C2 | semidirect |
| 5. #31773626 | C2 | semidirect |
| 6. #31773626 | C2 | semidirect |
| 7. #486×C271 | C2 | semidirect |
| 17. C4⋊(C271⋊C8) | C22 | semidirect |
| 18. C4⋊(C271⋊C8) | C22 | semidirect |
| 21. C4⋊Q8×C271 | C22 | semidirect |
| 24. C4×C8×C271 | C22 | semidirect |
| 60. D1084 | SD16 | semidirect |
| 109. C271 | #1639 | semidirect |
| 112. #486 | D271 | semidirect |
| 121. C4⋊Q8 | C2×D271 | semidirect |
| 134. C4×C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774532 | 2 |
| #31774174 | 2 |
| #31774099 | 2 |
| #31773641 | 2 |
| #31773626 | 2 |
| #486×C271 | 2 |
| #1639 | 271 |