Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #31774295 | C2 | semidirect |
| 4. #31774236 | C2 | semidirect |
| 5. #31774226 | C2 | semidirect |
| 6. #31774192 | C2 | semidirect |
| 7. #31774182 | C2 | semidirect |
| 8. #31774152 | C2 | semidirect |
| 10. #31773938 | C2 | semidirect |
| 11. C4×Q16×C271 | C2 | semidirect |
| 116. C271 | #3356 | semidirect |
| 126. C4×Q16 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774620 | 2 |
| #31774607 | 2 |
| #31774295 | 2 |
| #31774236 | 2 |
| #31774226 | 2 |
| #31774192 | 2 |
| #31774182 | 2 |
| #31774152 | 2 |
| #31773976 | 2 |
| #31773938 | 2 |
| C4×Q16×C271 | 2 |
| #3356 | 271 |