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 |
|---|---|---|
| 1. #31774380 | C2 | semidirect |
| 2. #31774235 | C2 | semidirect |
| 3. #31774230 | C2 | semidirect |
| 4. #31774218 | C2 | semidirect |
| 5. #31774208 | C2 | semidirect |
| 6. #31773937 | C2 | semidirect |
| 7. C2×#22576093 | C2 | semidirect |
| 8. #31773898 | C2 | semidirect |
| 9. #31773893 | C2 | semidirect |
| 10. #31773864 | C2 | semidirect |
| 133. C271 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774380 | 2 |
| #31774235 | 2 |
| #31774230 | 2 |
| #31774218 | 2 |
| #31774208 | 2 |
| #31773937 | 2 |
| C2×#22576093 | 2 |
| #31773898 | 2 |
| #31773893 | 2 |
| #31773864 | 2 |
| #537×C271 | 2 |
| #3098 | 271 |