Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
170 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 43 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. #31774335 | C2 | semidirect |
| 2. #31774333 | C2 | semidirect |
| 3. #31774272 | C2 | semidirect |
| 4. #31774013 | C2 | semidirect |
| 5. #31773717 | C2 | semidirect |
| 6. #31773709 | C2 | semidirect |
| 7. #361×C271 | C2 | semidirect |
| 26. Dic1084 | D4 | semidirect |
| 30. D2168 | D4 | semidirect |
| 77. C271 | #2213 | semidirect |
| 85. #361 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774335 | 2 |
| #31774333 | 2 |
| #31774272 | 2 |
| #31774013 | 2 |
| #31773717 | 2 |
| #31773709 | 2 |
| #361×C271 | 2 |
| #2213 | 271 |