Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C2×#22576208 | C2 | semidirect |
| 2. C2×#22576188 | C2 | semidirect |
| 3. C2×#22576149 | C2 | semidirect |
| 4. #31774072 | C2 | direct (N × H) |
| 5. C2×#22576086 | C2 | semidirect |
| 6. C2×#101×C271 | C2 | semidirect |
| 9. #22576208 | C22 | semidirect |
| 16. #22576188 | C22 | semidirect |
| 20. #22576149 | C22 | semidirect |
| 23. #22576086 | C22 | semidirect |
| 26. #101×C271 | C22 | semidirect |
| 113. C2×C271 | #454 | semidirect |
| 117. C271 | C2×#454 | semidirect |
| 124. C2×#101 | D271 | semidirect |
| 144. #101 | C2×D271 | semidirect |
| 233. C2 | #31774072 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576208 | 2 |
| C2×#22576188 | 2 |
| C2×#22576149 | 2 |
| #31774072 | 2 |
| C2×#22576086 | 2 |
| C2×#101×C271 | 2 |
| C2×#454 | 271 |