Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 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. C2×#22575482 | C2 | semidirect |
| 3. Q8×D1076 | C2 | semidirect |
| 4. #31770977 | C2 | semidirect |
| 5. #31770850 | C2 | semidirect |
| 6. #31770816 | C2 | semidirect |
| 7. #31770768 | C2 | semidirect |
| 8. #31770742 | C2 | semidirect |
| 9. C4×#16864392 | C2 | semidirect |
| 10. #31770682 | C2 | semidirect |
| 11. #460×C269 | C2 | semidirect |
| 56. #16864392 | D4 | semidirect |
| 124. C4×C269 | #137 | semidirect |
| 136. C269 | #3278 | semidirect |
| 144. #460 | D269 | semidirect |
| 265. C4 | #22575482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575482 | 2 |
| #31771275 | 2 |
| Q8×D1076 | 2 |
| #31770977 | 2 |
| #31770850 | 2 |
| #31770816 | 2 |
| #31770768 | 2 |
| #31770742 | 2 |
| C4×#16864392 | 2 |
| #31770682 | 2 |
| #460×C269 | 2 |
| #3278 | 269 |