Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×#16864638 | C2 | semidirect |
| 3. C2×#22576088 | C2 | direct (N × H) |
| 4. C22×C42×C271 | C2 | semidirect |
| 7. C2×#16864654 | C4 | semidirect |
| 9. C22×Dic542 | C4 | semidirect |
| 10. C22×D1084 | C4 | semidirect |
| 14. C2×#16864638 | C22 | semidirect |
| 16. #22576088 | C22 | direct (N × H) |
| 20. C2×C42×C271 | C22 | semidirect |
| 25. #16864654 | C2×C4 | semidirect |
| 28. C2×Dic542 | C2×C4 | semidirect |
| 30. C2×D1084 | C2×C4 | semidirect |
| 37. #16864638 | C23 | semidirect |
| 49. C42×C271 | C23 | semidirect |
| 53. Dic542 | C22×C4 | semidirect |
| 55. D1084 | C22×C4 | semidirect |
| 79. C22×C271 | #104 | semidirect |
| 93. C2×C271 | C2×#104 | semidirect |
| 96. C271 | C22×#104 | semidirect |
| 100. C22×C42 | D271 | semidirect |
| 116. C2×C42 | C2×D271 | semidirect |
| 146. C42 | C22×D271 | semidirect |
| 178. C22 | #22576088 | direct (N × H) |
| 191. C2 | C2×#22576088 | 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×#16864638 | 2 |
| C2×#22576088 | 2 |
| C22×C42×C271 | 2 |
| C22×#104 | 271 |