Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
390 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 97 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×#22575369 | C2 | semidirect |
| 3. #31770569 | C2 | semidirect |
| 4. #31770373 | C2 | semidirect |
| 5. C22×M16×C269 | C2 | semidirect |
| 50. M16×C269 | D4 | semidirect |
| 93. C22×C269 | #100 | semidirect |
| 113. C269 | #1900 | semidirect |
| 115. C22×M16 | D269 | semidirect |
| 159. M16 | C22⋊D269 | semidirect |
| 211. C22 | #22575369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575427 | 2 |
| C2×#22575369 | 2 |
| #31770569 | 2 |
| #31770373 | 2 |
| C22×M16×C269 | 2 |
| #1900 | 269 |