Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
312 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 95 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. #31773920 | C2 | semidirect |
| 4. C4×Dic271⋊C4 | C2 | semidirect |
| 5. #31773658 | C2 | semidirect |
| 6. #31773657 | C2 | semidirect |
| 9. Q8×Dic271 | C4 | semidirect |
| 10. Q8×Dic271 | C4 | semidirect |
| 13. D4×Dic271 | C4 | semidirect |
| 14. D4×Dic271 | C4 | semidirect |
| 86. Q8×C271 | C4⋊C4 | semidirect |
| 90. D4×C271 | C4⋊C4 | semidirect |
| 124. Dic271 | #104 | semidirect |
| 131. C271 | #1806 | semidirect |
| 204. Q8 | Dic271⋊C4 | semidirect |
| 208. D4 | Dic271⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic271 | 2 |
| #31773920 | 2 |
| C2×#22576087 | 2 |
| C4×Dic271⋊C4 | 2 |
| #31773658 | 2 |
| #31773657 | 2 |
| C2×#104×C271 | 2 |
| #1806 | 271 |