Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31774238 | C2 | semidirect |
| 3. #31774232 | C2 | semidirect |
| 4. #31774221 | C2 | semidirect |
| 5. #31774210 | C2 | semidirect |
| 6. #31773940 | C2 | semidirect |
| 7. C2×#22576093 | C2 | semidirect |
| 8. #31773896 | C2 | semidirect |
| 9. #31773891 | C2 | semidirect |
| 10. #31773864 | C2 | semidirect |
| 11. #520×C271 | C2 | semidirect |
| 133. C271 | #3098 | semidirect |
| 136. #520 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774475 | 2 |
| #31774238 | 2 |
| #31774232 | 2 |
| #31774221 | 2 |
| #31774210 | 2 |
| #31773940 | 2 |
| C2×#22576093 | 2 |
| #31773896 | 2 |
| #31773891 | 2 |
| #31773864 | 2 |
| #520×C271 | 2 |
| #3098 | 271 |