Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×#22575381 | C2 | semidirect |
| 3. C2×#22575380 | C2 | semidirect |
| 4. C2×#22575379 | C2 | semidirect |
| 5. M16×Dic269 | C2 | semidirect |
| 6. C4×#16864381 | C2 | semidirect |
| 7. C2×#104×C269 | C2 | semidirect |
| 10. #22575451 | C4 | semidirect |
| 11. #22575449 | C4 | semidirect |
| 12. #22575442 | C4 | semidirect |
| 13. #22575440 | C4 | semidirect |
| 45. #16864386 | D4 | semidirect |
| 71. M16×C269 | D4 | semidirect |
| 140. Dic269 | #104 | semidirect |
| 148. C269 | #1980 | semidirect |
| 154. C2×#104 | D269 | semidirect |
| 206. M16 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771151 | 2 |
| C2×#22575381 | 2 |
| C2×#22575380 | 2 |
| C2×#22575379 | 2 |
| M16×Dic269 | 2 |
| C4×#16864381 | 2 |
| C2×#104×C269 | 2 |
| #1980 | 269 |