Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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. #31774179 | C2 | semidirect |
| 4. #31773643 | C2 | semidirect |
| 5. #31773629 | C2 | semidirect |
| 7. #500×C271 | C2 | semidirect |
| 88. C271 | #1650 | semidirect |
| 91. #500 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774621 | 2 |
| #31774179 | 2 |
| #31774099 | 2 |
| #31773643 | 2 |
| #31773629 | 2 |
| #31773626 | 2 |
| #500×C271 | 2 |
| #1650 | 271 |