Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 2. #31774259 | C2 | semidirect |
| 3. #31774254 | C2 | semidirect |
| 4. #31773905 | C2 | semidirect |
| 6. C4×#16864638 | C2 | semidirect |
| 7. #533×C271 | C2 | semidirect |
| 15. #22576083 | C22 | semidirect |
| 17. #22576071 | C22 | semidirect |
| 18. C4×C271⋊C8 | C22 | semidirect |
| 19. C4⋊Q8×C271 | C22 | semidirect |
| 20. #125×C271 | C22 | semidirect |
| 83. C271 | #3140 | semidirect |
| 85. #533 | D271 | semidirect |
| 95. C4⋊Q8 | C2×D271 | semidirect |
| 96. #125 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576148 | 2 |
| #31774259 | 2 |
| #31774254 | 2 |
| #31773905 | 2 |
| #31773901 | 2 |
| C4×#16864638 | 2 |
| #533×C271 | 2 |
| #3140 | 271 |