Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 572 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. C2×#22576193 | C2 | semidirect |
| 2. C2×#22576188 | C2 | semidirect |
| 3. #31774447 | C2 | semidirect |
| 4. C2×#22576148 | C2 | semidirect |
| 5. #31774291 | C2 | semidirect |
| 6. #31774286 | C2 | semidirect |
| 7. #31774281 | C2 | semidirect |
| 8. C4×M16×C271 | C2 | semidirect |
| 14. C2×Dic1084 | C22 | semidirect |
| 16. C2×#16864643 | C22 | semidirect |
| 18. #22576160 | C22 | semidirect |
| 19. #22576157 | C22 | semidirect |
| 23. #22576148 | C22 | semidirect |
| 29. #97×C271 | C22 | semidirect |
| 30. C4×C8×C271 | C22 | semidirect |
| 56. M16×C271 | D4 | semidirect |
| 106. C271 | #3153 | semidirect |
| 115. C4×M16 | D271 | semidirect |
| 136. #97 | C2×D271 | semidirect |
| 137. C4×C8 | C2×D271 | semidirect |
| 159. M16 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576193 | 2 |
| C2×#22576188 | 2 |
| #31774447 | 2 |
| C2×#22576148 | 2 |
| #31774291 | 2 |
| #31774286 | 2 |
| #31774281 | 2 |
| C4×M16×C271 | 2 |
| #3153 | 271 |