Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#16864642 | C2 | semidirect |
| 2. #31774468 | C2 | semidirect |
| 3. #31774372 | C2 | semidirect |
| 4. #31774110 | C2 | semidirect |
| 5. #31774100 | C2 | semidirect |
| 6. #31773925 | C2 | semidirect |
| 7. #31773907 | C2 | semidirect |
| 8. #31773893 | C2 | semidirect |
| 14. #22576158 | C22 | semidirect |
| 15. #22576147 | C22 | semidirect |
| 23. Dic271⋊C8 | C22 | semidirect |
| 24. #22576085 | C22 | semidirect |
| 25. #22576084 | C22 | semidirect |
| 26. #22576081 | C22 | semidirect |
| 116. C271 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864642 | 2 |
| #31774468 | 2 |
| #31774372 | 2 |
| #31774110 | 2 |
| #31774100 | 2 |
| #31773925 | 2 |
| #31773907 | 2 |
| #31773893 | 2 |
| C2×AGL(1,ℤ/8)×C271 | 2 |
| #3042 | 271 |