Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
584 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#22575371 | C2 | semidirect |
| 3. C2×#22575369 | C2 | semidirect |
| 4. #31770569 | C2 | semidirect |
| 5. #407×C269 | C2 | semidirect |
| 103. C269 | #1785 | semidirect |
| 109. #407 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864402 | 2 |
| C2×#22575371 | 2 |
| C2×#22575369 | 2 |
| #31770569 | 2 |
| #407×C269 | 2 |
| #1785 | 269 |