Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31774663 | C2 | semidirect |
| 3. #31773903 | C2 | semidirect |
| 4. #31773901 | C2 | semidirect |
| 5. #31773870 | C2 | semidirect |
| 6. #31773653 | C2 | semidirect |
| 7. H(3,ℤ/4)×C271 | C2 | semidirect |
| 14. #22576157 | C4 | semidirect |
| 15. #22576148 | C4 | semidirect |
| 44. C2×C271⋊C8 | D4 | semidirect |
| 53. C2×C8×C271 | D4 | semidirect |
| 115. C271 | #1910 | semidirect |
| 123. H(3,ℤ/4) | D271 | semidirect |
| 165. C2×C8 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774663 | 2 |
| #31774466 | 2 |
| #31773903 | 2 |
| #31773901 | 2 |
| #31773870 | 2 |
| #31773653 | 2 |
| H(3,ℤ/4)×C271 | 2 |
| #1910 | 271 |