Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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. #31770629 | C2 | semidirect |
| 3. C2×#22575381 | C2 | semidirect |
| 4. C43×C269 | C2 | semidirect |
| 7. #22575453 | C4 | semidirect |
| 8. #22575450 | C4 | semidirect |
| 9. #22575441 | C4 | semidirect |
| 36. C42×C269 | D4 | semidirect |
| 63. C4×C269 | #104 | semidirect |
| 72. C269 | #1962 | semidirect |
| 77. C43 | D269 | semidirect |
| 109. C42 | D1076 | semidirect |
| 137. C4 | #22575381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771155 | 2 |
| #31770629 | 2 |
| C2×#22575381 | 2 |
| C43×C269 | 2 |
| #1962 | 269 |