Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16864654 | C2 | semidirect |
| 2. C22×#16864642 | C2 | semidirect |
| 3. C22×#16864639 | C2 | semidirect |
| 4. #31774040 | C2 | direct (N × H) |
| 5. C2×#22576083 | C2 | semidirect |
| 6. C2×#22576080 | C2 | semidirect |
| 7. C2×C22⋊(C271⋊C8) | C2 | semidirect |
| 8. C2×#121×C271 | C2 | semidirect |
| 12. C2×#16864654 | C22 | semidirect |
| 18. C2×#16864642 | C22 | semidirect |
| 20. C2×#16864639 | C22 | semidirect |
| 23. #22576083 | C22 | semidirect |
| 24. #22576080 | C22 | semidirect |
| 25. C22⋊(C271⋊C8) | C22 | semidirect |
| 30. #121×C271 | C22 | semidirect |
| 39. C2×Dic542 | D4 | semidirect |
| 43. C2×D1084 | D4 | semidirect |
| 80. Dic542 | C2×D4 | semidirect |
| 83. D1084 | C2×D4 | semidirect |
| 138. C2×C271 | #449 | semidirect |
| 143. C271 | C2×#449 | semidirect |
| 148. C2×#121 | D271 | semidirect |
| 171. #121 | C2×D271 | semidirect |
| 283. C2 | #31774040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864654 | 2 |
| C22×#16864642 | 2 |
| C22×#16864639 | 2 |
| #31774040 | 2 |
| C2×#22576083 | 2 |
| C2×#22576080 | 2 |
| C2×C22⋊(C271⋊C8) | 2 |
| C2×#121×C271 | 2 |
| C2×#449 | 271 |