Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31774293 | C2 | semidirect |
| 3. #31774235 | C2 | semidirect |
| 4. #31774227 | C2 | semidirect |
| 5. #31774189 | C2 | semidirect |
| 6. #31774182 | C2 | semidirect |
| 7. #31774153 | C2 | semidirect |
| 8. C4×#16864644 | C2 | semidirect |
| 10. #31773937 | C2 | semidirect |
| 116. C271 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774617 | 2 |
| #31774293 | 2 |
| #31774235 | 2 |
| #31774227 | 2 |
| #31774189 | 2 |
| #31774182 | 2 |
| #31774153 | 2 |
| C4×#16864644 | 2 |
| #31773975 | 2 |
| #31773937 | 2 |
| #554×C271 | 2 |
| #3356 | 271 |