Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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×#22576191 | C2 | semidirect |
| 3. #31773914 | C2 | semidirect |
| 4. #31773906 | C2 | semidirect |
| 5. #31773870 | C2 | semidirect |
| 6. #31773667 | C2 | semidirect |
| 7. #536×C271 | C2 | semidirect |
| 136. C271 | #2009 | semidirect |
| 140. #536 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774695 | 2 |
| C2×#22576191 | 2 |
| #31773914 | 2 |
| #31773906 | 2 |
| #31773870 | 2 |
| #31773667 | 2 |
| #536×C271 | 2 |
| #2009 | 271 |