Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22575476 | C2 | semidirect |
| 2. C2×Q16×D269 | C2 | semidirect |
| 3. #31771267 | C2 | semidirect |
| 4. #31770989 | C2 | semidirect |
| 5. #31770847 | C2 | semidirect |
| 6. #31770842 | C2 | semidirect |
| 7. #31770827 | C2 | semidirect |
| 8. #31770770 | C2 | semidirect |
| 9. #31770745 | C2 | semidirect |
| 10. C8×D1076 | C2 | semidirect |
| 11. C4×Q16×C269 | C2 | semidirect |
| 73. Q16×C269 | D4 | semidirect |
| 120. C2×D269 | #135 | semidirect |
| 136. C269 | #3285 | semidirect |
| 147. C4×Q16 | D269 | semidirect |
| 195. Q16 | D1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575476 | 2 |
| C2×Q16×D269 | 2 |
| #31771267 | 2 |
| #31770989 | 2 |
| #31770847 | 2 |
| #31770842 | 2 |
| #31770827 | 2 |
| #31770770 | 2 |
| #31770745 | 2 |
| C8×D1076 | 2 |
| C4×Q16×C269 | 2 |
| #3285 | 269 |