Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
524 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 149 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×D2168 | C2 | semidirect |
| 2. #31774461 | C2 | semidirect |
| 3. #31774150 | C2 | semidirect |
| 4. #31774133 | C2 | semidirect |
| 5. #31773935 | C2 | semidirect |
| 6. #31773903 | C2 | semidirect |
| 7. C2×#131×C271 | C2 | semidirect |
| 14. #22576134 | C22 | semidirect |
| 17. #22576094 | C22 | semidirect |
| 18. #22576092 | C22 | semidirect |
| 19. #22576082 | C22 | semidirect |
| 23. C2×M16×C271 | C22 | semidirect |
| 25. C22×C8×C271 | C22 | semidirect |
| 48. C2×C8×C271 | D4 | semidirect |
| 93. C271 | #3058 | semidirect |
| 96. C2×#131 | D271 | semidirect |
| 109. C2×M16 | C2×D271 | semidirect |
| 111. C22×C8 | C2×D271 | semidirect |
| 138. C2×C8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2168 | 2 |
| #31774461 | 2 |
| #31774150 | 2 |
| #31774133 | 2 |
| #31773935 | 2 |
| #31773903 | 2 |
| C2×#131×C271 | 2 |
| #3058 | 271 |