Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×#16864638 | C2 | semidirect |
| 4. #31773657 | C2 | semidirect |
| 5. C43×C271 | C2 | semidirect |
| 8. C4×Dic542 | C4 | semidirect |
| 9. C4×D1084 | C4 | semidirect |
| 14. #22576088 | C4 | direct (N × H) |
| 28. #16864638 | C2×C4 | semidirect |
| 42. C42×C271 | C2×C4 | semidirect |
| 47. Dic542 | C42 | semidirect |
| 49. D1084 | C42 | semidirect |
| 73. C4×C271 | #104 | semidirect |
| 83. C271 | C4×#104 | semidirect |
| 88. C43 | D271 | semidirect |
| 126. C42 | C4×D271 | semidirect |
| 159. C4 | #22576088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864654 | 2 |
| C2×#22576088 | 2 |
| C4×#16864638 | 2 |
| #31773657 | 2 |
| C43×C271 | 2 |
| C4×#104 | 271 |