Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 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. #31773801 | C2 | semidirect |
| 3. #31773789 | C2 | semidirect |
| 4. #31773786 | C2 | semidirect |
| 6. #31773771 | C2 | semidirect |
| 7. C4×C4⋊Dic271 | C2 | semidirect |
| 8. #31773744 | C2 | semidirect |
| 9. #383×C271 | C2 | semidirect |
| 13. #22576148 | C4 | semidirect |
| 34. C2×Dic542 | C2×C4 | semidirect |
| 48. (C2×D271)⋊C4 | C2×C4 | semidirect |
| 49. (C2×D271)⋊C4 | C2×C4 | semidirect |
| 58. C42×C271 | C2×C4 | semidirect |
| 118. C271 | #2337 | semidirect |
| 126. #383 | D271 | semidirect |
| 177. C42 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576148 | 2 |
| #31773801 | 2 |
| #31773789 | 2 |
| #31773786 | 2 |
| #31773775 | 2 |
| #31773771 | 2 |
| C4×C4⋊Dic271 | 2 |
| #31773744 | 2 |
| #383×C271 | 2 |
| #2337 | 271 |