Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
1224 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 277 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. C2×C4×C22⋊D271 | C2 | semidirect |
| 3. #31773776 | C2 | semidirect |
| 4. #31773770 | C2 | semidirect |
| 5. #31773753 | C2 | semidirect |
| 6. C4×C22⋊Dic271 | C2 | semidirect |
| 7. C24×C4×C271 | C2 | semidirect |
| 9. C22×C4×D271 | C22 | semidirect |
| 10. #22576129 | C4 | direct (N × H) |
| 12. C2×Dic271⋊C4 | C22 | semidirect |
| 16. C2×(C2×D271)⋊C4 | C22 | semidirect |
| 17. C2×C4×Dic271 | C22 | semidirect |
| 18. C271⋊#95 | C22 | semidirect |
| 26. C2×C22⋊D271 | C2×C4 | semidirect |
| 34. C22⋊Dic271 | C2×C4 | semidirect |
| 39. C24×C271 | C2×C4 | semidirect |
| 45. C22×C4×C271 | D4 | semidirect |
| 50. C22×D271 | C22×C4 | semidirect |
| 57. C2×Dic271 | C22×C4 | semidirect |
| 78. C22×C271 | C4×D4 | semidirect |
| 86. C4×C271 | #120 | semidirect |
| 95. C271 | C4×#120 | semidirect |
| 97. C24×C4 | D271 | semidirect |
| 122. C24 | C4×D271 | semidirect |
| 135. C22×C4 | C22⋊D271 | semidirect |
| 177. C22 | C4×C22⋊D271 | semidirect |
| 185. C4 | #22576129 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576129 | 2 |
| C2×C4×C22⋊D271 | 2 |
| #31773776 | 2 |
| #31773770 | 2 |
| #31773753 | 2 |
| C4×C22⋊Dic271 | 2 |
| C24×C4×C271 | 2 |
| C4×#120 | 271 |