Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#22576168 | C2 | semidirect |
| 3. #31774473 | C2 | semidirect |
| 5. #31774142 | C2 | semidirect |
| 6. #31774125 | C2 | semidirect |
| 7. #31773933 | C2 | semidirect |
| 8. #31773907 | C2 | semidirect |
| 9. #418×C271 | C2 | semidirect |
| 16. C2×#16864637 | C22 | semidirect |
| 18. C2×C8×D271 | C22 | semidirect |
| 24. #22576140 | C22 | semidirect |
| 28. #22576093 | C22 | semidirect |
| 29. #22576091 | C22 | semidirect |
| 30. #22576085 | C22 | semidirect |
| 50. C2×C271⋊C8 | D4 | semidirect |
| 120. C271 | #3057 | semidirect |
| 130. #418 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864642 | 2 |
| C2×#22576168 | 2 |
| #31774473 | 2 |
| #31774464 | 2 |
| #31774142 | 2 |
| #31774125 | 2 |
| #31773933 | 2 |
| #31773907 | 2 |
| #418×C271 | 2 |
| #3057 | 271 |