Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×Q16×D269 | C2 | semidirect |
| 4. #31770862 | C2 | semidirect |
| 5. #31770861 | C2 | semidirect |
| 6. #31770847 | C2 | semidirect |
| 7. #31770846 | C2 | semidirect |
| 8. #31770843 | C2 | semidirect |
| 9. #31770642 | C2 | semidirect |
| 10. #31770612 | C2 | semidirect |
| 11. #467×C269 | C2 | semidirect |
| 137. C269 | #3059 | semidirect |
| 147. #467 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D269 | 2 |
| C2×#22575459 | 2 |
| #31771178 | 2 |
| #31770862 | 2 |
| #31770861 | 2 |
| #31770847 | 2 |
| #31770846 | 2 |
| #31770843 | 2 |
| #31770642 | 2 |
| #31770612 | 2 |
| #467×C269 | 2 |
| #3059 | 269 |