Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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. #31773861 | C2 | semidirect |
| 2. C4×C22⋊Dic271 | C2 | semidirect |
| 3. #31773631 | C2 | semidirect |
| 9. C22⋊(C271⋊C8) | C22 | semidirect |
| 10. C271⋊#95 | C22 | semidirect |
| 12. C22×D4×C271 | C4 | semidirect |
| 16. #121×C271 | C4 | semidirect |
| 18. C2×C4⋊C4×C271 | C4 | semidirect |
| 103. C271 | #1507 | semidirect |
| 110. C22×D4 | Dic271 | semidirect |
| 115. #121 | Dic271 | semidirect |
| 117. C2×C4⋊C4 | Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31773861 | 2 |
| C4×C22⋊Dic271 | 2 |
| #31773631 | 2 |
| C2×#121×C271 | 2 |
| #1507 | 271 |