Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
260 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 73 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. #31770627 | C2 | semidirect |
| 3. C4⋊C8×D269 | C2 | semidirect |
| 4. #31770352 | C2 | semidirect |
| 5. #31770350 | C2 | semidirect |
| 6. #31770349 | C2 | semidirect |
| 7. #331×C269 | C2 | semidirect |
| 98. C269 | #1547 | semidirect |
| 106. #331 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771153 | 2 |
| #31770627 | 2 |
| C4⋊C8×D269 | 2 |
| #31770352 | 2 |
| #31770350 | 2 |
| #31770349 | 2 |
| #331×C269 | 2 |
| #1547 | 269 |