Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
412 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 189 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. #31773956 | C2 | direct (N × H) |
| 3. C2×Dic271⋊C8 | C2 | semidirect |
| 5. C2×#22576071 | C2 | semidirect |
| 6. C2×C4×C8×C271 | C2 | semidirect |
| 14. Dic271⋊C8 | C22 | semidirect |
| 16. #22576071 | C22 | semidirect |
| 19. C4×C8×C271 | C22 | semidirect |
| 66. C2×C271 | #433 | semidirect |
| 70. C271 | C2×#433 | semidirect |
| 77. C2×C4×C8 | D271 | semidirect |
| 90. C4×C8 | C2×D271 | semidirect |
| 138. C2 | #31773956 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576117 | 2 |
| #31773956 | 2 |
| C2×Dic271⋊C8 | 2 |
| C2×(C2×D271)⋊C8 | 2 |
| C2×#22576071 | 2 |
| C2×C4×C8×C271 | 2 |
| C2×#433 | 271 |