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×#22576190 | C2 | semidirect |
| 2. C2×#22576147 | C2 | semidirect |
| 3. #41×Dic271 | C2 | semidirect |
| 4. #31774117 | C2 | semidirect |
| 5. #31774110 | C2 | semidirect |
| 6. #31773920 | C2 | semidirect |
| 7. #31773907 | C2 | semidirect |
| 8. #31773902 | C2 | semidirect |
| 12. C2×#16864644 | C22 | semidirect |
| 13. C2×#16864642 | C22 | semidirect |
| 18. Q8×Dic271 | C22 | semidirect |
| 20. D4×Dic271 | C22 | semidirect |
| 26. Dic271⋊C8 | C22 | semidirect |
| 27. #22576085 | C22 | semidirect |
| 125. C271 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576190 | 2 |
| C2×#22576147 | 2 |
| #41×Dic271 | 2 |
| #31774117 | 2 |
| #31774110 | 2 |
| #31773920 | 2 |
| #31773907 | 2 |
| #31773902 | 2 |
| C2×AGL(1,ℤ/8)×C271 | 2 |
| #3040 | 271 |