Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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. #31770653 | C2 | semidirect |
| 5. M16×Dic269 | C2 | semidirect |
| 6. #31770364 | C2 | semidirect |
| 7. #344×C269 | C2 | semidirect |
| 16. #22575371 | C4 | semidirect |
| 17. #22575369 | C4 | semidirect |
| 95. C269 | #1932 | semidirect |
| 102. #344 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31770653 | 2 |
| #31770623 | 2 |
| C2×#22575379 | 2 |
| #31770587 | 2 |
| M16×Dic269 | 2 |
| #31770364 | 2 |
| #344×C269 | 2 |
| #1932 | 269 |