Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774607 | C2 | semidirect |
| 3. #31774302 | C2 | semidirect |
| 4. #31774237 | C2 | semidirect |
| 5. #31774209 | C2 | semidirect |
| 6. #31774192 | C2 | semidirect |
| 7. #31774187 | C2 | semidirect |
| 8. #31774140 | C2 | semidirect |
| 9. #31773976 | C2 | semidirect |
| 10. #31773936 | C2 | semidirect |
| 11. C4×SD16×C271 | C2 | semidirect |
| 121. C271 | #3357 | semidirect |
| 131. C4×SD16 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774612 | 2 |
| #31774607 | 2 |
| #31774302 | 2 |
| #31774237 | 2 |
| #31774209 | 2 |
| #31774192 | 2 |
| #31774187 | 2 |
| #31774140 | 2 |
| #31773976 | 2 |
| #31773936 | 2 |
| C4×SD16×C271 | 2 |
| #3357 | 271 |