Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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×#22576082 | C2 | semidirect |
| 3. C2×#22576081 | C2 | semidirect |
| 4. C2×#22576080 | C2 | semidirect |
| 5. C2×#22576070 | C2 | semidirect |
| 6. #31773762 | C2 | semidirect |
| 7. C2×#102×C271 | C2 | semidirect |
| 12. #22576156 | C4 | semidirect |
| 38. C2×C271⋊C8 | D4 | semidirect |
| 54. C2×C8×C271 | D4 | semidirect |
| 121. C271 | #1961 | semidirect |
| 127. C2×#102 | D271 | semidirect |
| 172. C2×C8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576156 | 2 |
| C2×#22576082 | 2 |
| C2×#22576081 | 2 |
| C2×#22576080 | 2 |
| C2×#22576070 | 2 |
| #31773762 | 2 |
| C2×#102×C271 | 2 |
| #1961 | 271 |