Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31771086 | C2 | semidirect |
| 5. #31770826 | C2 | semidirect |
| 6. #31770819 | C2 | semidirect |
| 7. #31770814 | C2 | semidirect |
| 8. #31770809 | C2 | semidirect |
| 9. #31770633 | C2 | semidirect |
| 10. C2×#22575376 | C2 | semidirect |
| 11. #417×C269 | C2 | semidirect |
| 146. C269 | #3046 | semidirect |
| 157. #417 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575486 | 2 |
| C2×#22575473 | 2 |
| #31771176 | 2 |
| #31771086 | 2 |
| #31770826 | 2 |
| #31770819 | 2 |
| #31770814 | 2 |
| #31770809 | 2 |
| #31770633 | 2 |
| C2×#22575376 | 2 |
| #417×C269 | 2 |
| #3046 | 269 |