Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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×#22575364 | C2 | semidirect |
| 3. #31770346 | C2 | semidirect |
| 4. #31770344 | C2 | semidirect |
| 5. C4×M16×C269 | C2 | semidirect |
| 91. C269 | #1524 | semidirect |
| 94. C4×M16 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771139 | 2 |
| C2×#22575364 | 2 |
| #31770346 | 2 |
| #31770344 | 2 |
| C4×M16×C269 | 2 |
| #1524 | 269 |