Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22575486 | C2 | semidirect |
| 3. #31771176 | C2 | semidirect |
| 4. #31770863 | C2 | semidirect |
| 5. #31770851 | C2 | semidirect |
| 6. #31770846 | C2 | semidirect |
| 7. #31770834 | C2 | semidirect |
| 8. #31770647 | C2 | semidirect |
| 9. #31770602 | C2 | semidirect |
| 10. C2×#22575378 | C2 | semidirect |
| 11. C2×#131×C269 | C2 | semidirect |
| 79. M16×C269 | D4 | semidirect |
| 143. C269 | #3063 | semidirect |
| 146. C2×#131 | D269 | semidirect |
| 210. M16 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575486 | 2 |
| #31771183 | 2 |
| #31771176 | 2 |
| #31770863 | 2 |
| #31770851 | 2 |
| #31770846 | 2 |
| #31770834 | 2 |
| #31770647 | 2 |
| #31770602 | 2 |
| C2×#22575378 | 2 |
| C2×#131×C269 | 2 |
| #3063 | 269 |