Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31774378 | C2 | semidirect |
| 3. #31774236 | C2 | semidirect |
| 4. #31774231 | C2 | semidirect |
| 5. #31774220 | C2 | semidirect |
| 6. #31774209 | C2 | semidirect |
| 7. #31773939 | C2 | semidirect |
| 8. C2×#22576093 | C2 | semidirect |
| 9. #31773893 | C2 | semidirect |
| 10. #31773865 | C2 | semidirect |
| 11. #417×C271 | C2 | semidirect |
| 133. C271 | #3098 | semidirect |
| 143. #417 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774475 | 2 |
| #31774378 | 2 |
| #31774236 | 2 |
| #31774231 | 2 |
| #31774220 | 2 |
| #31774209 | 2 |
| #31773939 | 2 |
| C2×#22576093 | 2 |
| #31773893 | 2 |
| #31773865 | 2 |
| #417×C271 | 2 |
| #3098 | 271 |