Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31771139 | C2 | semidirect |
| 2. #31770913 | C2 | semidirect |
| 3. #31770906 | C2 | semidirect |
| 4. #31770846 | C2 | semidirect |
| 6. #31770834 | C2 | semidirect |
| 7. #31770828 | C2 | semidirect |
| 8. #31770821 | C2 | semidirect |
| 9. C2×C4⋊C8×C269 | C2 | semidirect |
| 106. C269 | #3250 | semidirect |
| 116. C2×C4⋊C8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771139 | 2 |
| #31770913 | 2 |
| #31770906 | 2 |
| #31770846 | 2 |
| #31770841 | 2 |
| #31770834 | 2 |
| #31770828 | 2 |
| #31770821 | 2 |
| C2×C4⋊C8×C269 | 2 |
| #3250 | 269 |