Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. C2×#22575451 | C2 | semidirect |
| 5. #31770814 | C2 | semidirect |
| 6. #31770809 | C2 | semidirect |
| 7. #31770628 | C2 | semidirect |
| 8. #31770613 | C2 | semidirect |
| 9. #419×C269 | C2 | semidirect |
| 116. Dic269 | #137 | semidirect |
| 121. C269 | #3039 | semidirect |
| 131. #419 | 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×#22575484 | 2 |
| C2×#22575451 | 2 |
| #31771073 | 2 |
| #31770814 | 2 |
| #31770809 | 2 |
| #31770628 | 2 |
| #31770613 | 2 |
| #419×C269 | 2 |
| #3039 | 269 |