Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
458 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×C4⋊C4×D271 | C2 | semidirect |
| 3. #31774231 | C2 | semidirect |
| 4. #31774226 | C2 | semidirect |
| 5. #31774214 | C2 | semidirect |
| 6. #31774209 | C2 | semidirect |
| 7. #31773939 | C2 | semidirect |
| 8. #31773937 | C2 | semidirect |
| 9. #31773898 | C2 | semidirect |
| 10. #31773860 | C2 | semidirect |
| 11. #417×C271 | C2 | semidirect |
| 30. #22576094 | C22 | semidirect |
| 31. #22576093 | C22 | semidirect |
| 32. #22576092 | C22 | semidirect |
| 33. #22576091 | C22 | semidirect |
| 34. #22576084 | C22 | semidirect |
| 35. #22576081 | C22 | semidirect |
| 41. #103×C271 | C22 | semidirect |
| 42. #102×C271 | C22 | semidirect |
| 155. C271 | #3092 | semidirect |
| 166. #417 | D271 | semidirect |
| 194. #103 | C2×D271 | semidirect |
| 196. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774404 | 2 |
| C2×C4⋊C4×D271 | 2 |
| #31774231 | 2 |
| #31774226 | 2 |
| #31774214 | 2 |
| #31774209 | 2 |
| #31773939 | 2 |
| #31773937 | 2 |
| #31773898 | 2 |
| #31773860 | 2 |
| #417×C271 | 2 |
| #3092 | 271 |