Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31770949 | C2 | semidirect |
| 4. #31770937 | C2 | semidirect |
| 5. #31770897 | C2 | semidirect |
| 6. #31770887 | C2 | semidirect |
| 7. #31770864 | C2 | semidirect |
| 8. C4×Dic1076 | C2 | semidirect |
| 10. #31770644 | C2 | semidirect |
| 11. #498×C269 | C2 | semidirect |
| 116. C269 | #3356 | semidirect |
| 120. #498 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771329 | 2 |
| #31771316 | 2 |
| #31770949 | 2 |
| #31770937 | 2 |
| #31770897 | 2 |
| #31770887 | 2 |
| #31770864 | 2 |
| C4×Dic1076 | 2 |
| #31770684 | 2 |
| #31770644 | 2 |
| #498×C269 | 2 |
| #3356 | 269 |