Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31771233 | C2 | semidirect |
| 3. #31770972 | C2 | semidirect |
| 4. #31770963 | C2 | semidirect |
| 5. #31770958 | C2 | semidirect |
| 6. #31770954 | C2 | semidirect |
| 7. #31770613 | C2 | semidirect |
| 9. C2×#22575378 | C2 | semidirect |
| 10. #31770560 | C2 | semidirect |
| 127. C269 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771233 | 2 |
| #31771176 | 2 |
| #31770972 | 2 |
| #31770963 | 2 |
| #31770958 | 2 |
| #31770954 | 2 |
| #31770613 | 2 |
| #31770606 | 2 |
| C2×#22575378 | 2 |
| #31770560 | 2 |
| #416×C269 | 2 |
| #3137 | 269 |