Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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. #31774239 | C2 | semidirect |
| 4. #31774233 | C2 | semidirect |
| 5. #31774228 | C2 | semidirect |
| 6. #31773939 | C2 | semidirect |
| 7. #31773907 | C2 | semidirect |
| 25. #22576094 | C22 | semidirect |
| 26. #22576092 | C22 | semidirect |
| 27. #22576085 | C22 | semidirect |
| 28. #22576085 | C22 | semidirect |
| 116. C271 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576139 | 2 |
| C2×#22576119 | 2 |
| #31774239 | 2 |
| #31774233 | 2 |
| #31774228 | 2 |
| #31773939 | 2 |
| #31773907 | 2 |
| #407×C271 | 2 |
| #3095 | 271 |