Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#16864642 | C2 | semidirect |
| 2. C22×#16864638 | C2 | semidirect |
| 3. C2×#22576139 | C2 | semidirect |
| 4. #31774141 | C2 | direct (N × H) |
| 5. C2×#22576093 | C2 | semidirect |
| 6. C2×#22576083 | C2 | semidirect |
| 7. C2×#22576081 | C2 | semidirect |
| 11. C2×#16864642 | C22 | semidirect |
| 13. C2×#16864638 | C22 | semidirect |
| 17. #22576139 | C22 | semidirect |
| 21. #22576093 | C22 | semidirect |
| 22. #22576083 | C22 | semidirect |
| 23. #22576081 | C22 | semidirect |
| 40. C2×C271⋊C8 | D4 | semidirect |
| 73. C271⋊C8 | C2×D4 | semidirect |
| 119. C2×C271 | #468 | semidirect |
| 123. C271 | C2×#468 | semidirect |
| 243. C2 | #31774141 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864642 | 2 |
| C22×#16864638 | 2 |
| C2×#22576139 | 2 |
| #31774141 | 2 |
| C2×#22576093 | 2 |
| C2×#22576083 | 2 |
| C2×#22576081 | 2 |
| C2×#121×C271 | 2 |
| C2×#468 | 271 |