Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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. #31773939 | C2 | semidirect |
| 5. #31773852 | C2 | semidirect |
| 6. #31773665 | C2 | semidirect |
| 7. #341×C271 | C2 | semidirect |
| 18. #22576076 | C4 | semidirect |
| 100. C271 | #1931 | semidirect |
| 108. #341 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31773939 | 2 |
| #31773903 | 2 |
| C2×#22576082 | 2 |
| C2×#22576076 | 2 |
| #31773852 | 2 |
| #31773665 | 2 |
| #341×C271 | 2 |
| #1931 | 271 |