Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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. #31770979 | C2 | semidirect |
| 4. #31770853 | C2 | semidirect |
| 5. #31770812 | C2 | semidirect |
| 6. #31770805 | C2 | semidirect |
| 7. #31770765 | C2 | semidirect |
| 8. #31770744 | C2 | semidirect |
| 9. C4×#16864392 | C2 | semidirect |
| 10. #31770683 | C2 | semidirect |
| 11. D4×Q8×C269 | C2 | semidirect |
| 52. #16864392 | D4 | semidirect |
| 126. C4×C269 | #137 | semidirect |
| 136. C269 | #3278 | semidirect |
| 140. D4×Q8 | D269 | semidirect |
| 265. 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 |
| #31771276 | 2 |
| #31770979 | 2 |
| #31770853 | 2 |
| #31770812 | 2 |
| #31770805 | 2 |
| #31770765 | 2 |
| #31770744 | 2 |
| C4×#16864392 | 2 |
| #31770683 | 2 |
| D4×Q8×C269 | 2 |
| #3278 | 269 |