Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. C2×#22576084 | C2 | semidirect |
| 5. #31773660 | C2 | semidirect |
| 6. #31773659 | C2 | semidirect |
| 7. C2×#103×C271 | C2 | semidirect |
| 12. #22576136 | C4 | semidirect |
| 44. C4⋊Dic271 | C2×C4 | semidirect |
| 54. C2×Q8×C271 | C2×C4 | semidirect |
| 116. C2×D271 | #103 | semidirect |
| 134. C271 | #1872 | semidirect |
| 139. C2×#103 | D271 | semidirect |
| 167. C2×Q8 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576136 | 2 |
| C2×C4⋊C4×D271 | 2 |
| C2×#22576084 | 2 |
| C2×(C2×D271)⋊C8 | 2 |
| #31773660 | 2 |
| #31773659 | 2 |
| C2×#103×C271 | 2 |
| #1872 | 271 |