Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. Q8×Dic538 | C2 | semidirect |
| 3. #31770951 | C2 | semidirect |
| 4. #31770950 | C2 | semidirect |
| 5. #31770896 | C2 | semidirect |
| 6. #31770893 | C2 | semidirect |
| 7. #31770803 | C2 | semidirect |
| 8. #31770729 | C2 | semidirect |
| 9. SD16×Dic269 | C2 | semidirect |
| 10. C4×#16864389 | C2 | semidirect |
| 11. #460×C269 | C2 | semidirect |
| 77. Dic538 | SD16 | semidirect |
| 92. Q8×C269 | #41 | semidirect |
| 125. C269 | #3362 | semidirect |
| 134. #460 | D269 | semidirect |
| 206. Q8 | #16864401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic538 | 2 |
| #31771275 | 2 |
| #31770951 | 2 |
| #31770950 | 2 |
| #31770896 | 2 |
| #31770893 | 2 |
| #31770803 | 2 |
| #31770729 | 2 |
| SD16×Dic269 | 2 |
| C4×#16864389 | 2 |
| #460×C269 | 2 |
| #3362 | 269 |