Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#22575484 | C2 | semidirect |
| 3. #31770984 | C2 | semidirect |
| 4. #31770861 | C2 | semidirect |
| 5. #31770815 | C2 | semidirect |
| 6. #31770807 | C2 | semidirect |
| 7. #31770765 | C2 | semidirect |
| 8. #31770761 | C2 | semidirect |
| 9. C4×#16864389 | C2 | semidirect |
| 10. #31770683 | C2 | semidirect |
| 11. D4×Q8×C269 | C2 | semidirect |
| 53. #16864389 | D4 | semidirect |
| 124. C4×C269 | #137 | semidirect |
| 134. C269 | #3276 | semidirect |
| 137. D4×Q8 | D269 | semidirect |
| 261. C4 | #22575484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575484 | 2 |
| #31771260 | 2 |
| #31770984 | 2 |
| #31770861 | 2 |
| #31770815 | 2 |
| #31770807 | 2 |
| #31770765 | 2 |
| #31770761 | 2 |
| C4×#16864389 | 2 |
| #31770683 | 2 |
| D4×Q8×C269 | 2 |
| #3276 | 269 |