Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
422 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 205 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. #31773969 | C2 | semidirect |
| 2. D4×C271⋊C8 | C2 | semidirect |
| 3. #31773958 | C2 | semidirect |
| 4. #31773864 | C2 | semidirect |
| 5. C2×C22⋊(C271⋊C8) | C2 | semidirect |
| 7. C2×#16864638 | C22 | semidirect |
| 9. C22×C271⋊C8 | C22 | semidirect |
| 10. C4⋊(C271⋊C8) | C22 | semidirect |
| 14. C22⋊(C271⋊C8) | C22 | semidirect |
| 15. #22576071 | C22 | semidirect |
| 16. C4×C271⋊C8 | C22 | semidirect |
| 89. C271 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31773969 | 2 |
| D4×C271⋊C8 | 2 |
| #31773958 | 2 |
| #31773864 | 2 |
| C2×C22⋊(C271⋊C8) | 2 |
| #525×C271 | 2 |
| #2977 | 271 |