Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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×#22576117 | C2 | semidirect |
| 3. C2×#22576087 | C2 | semidirect |
| 4. #31773860 | C2 | semidirect |
| 5. #31773658 | C2 | semidirect |
| 6. #31773657 | C2 | semidirect |
| 7. C2×#104×C271 | C2 | semidirect |
| 11. #22576136 | C4 | semidirect |
| 12. #22576131 | C4 | semidirect |
| 49. C4×Dic271 | D4 | semidirect |
| 64. C42×C271 | D4 | semidirect |
| 127. C271 | #1897 | semidirect |
| 132. C2×#104 | D271 | semidirect |
| 192. C42 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774404 | 2 |
| C2×#22576117 | 2 |
| C2×#22576087 | 2 |
| #31773860 | 2 |
| #31773658 | 2 |
| #31773657 | 2 |
| C2×#104×C271 | 2 |
| #1897 | 271 |