Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
596 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 177 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. #31773797 | C2 | semidirect |
| 3. #31773786 | C2 | semidirect |
| 4. #31773782 | C2 | semidirect |
| 5. #31773775 | C2 | semidirect |
| 6. #31773773 | C2 | semidirect |
| 7. C4×C22⋊Dic271 | C2 | semidirect |
| 8. #31773744 | C2 | semidirect |
| 9. #381×C271 | C2 | semidirect |
| 13. #22576134 | C4 | semidirect |
| 38. C2×C22⋊D271 | C2×C4 | semidirect |
| 45. C4⋊Dic271 | C2×C4 | semidirect |
| 51. (C2×D271)⋊C4 | C2×C4 | semidirect |
| 58. C22×C4×C271 | C2×C4 | semidirect |
| 134. C271 | #2333 | semidirect |
| 142. #381 | D271 | semidirect |
| 183. C22×C4 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576134 | 2 |
| #31773797 | 2 |
| #31773786 | 2 |
| #31773782 | 2 |
| #31773775 | 2 |
| #31773773 | 2 |
| C4×C22⋊Dic271 | 2 |
| #31773744 | 2 |
| #381×C271 | 2 |
| #2333 | 271 |