Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 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. #31770509 | C2 | semidirect |
| 3. #31770496 | C2 | semidirect |
| 4. #31770495 | C2 | semidirect |
| 6. #31770476 | C2 | semidirect |
| 7. #31770473 | C2 | semidirect |
| 8. C4×#16864379 | C2 | semidirect |
| 9. C4×C4⋊C4×C269 | C2 | semidirect |
| 13. #22575441 | C4 | semidirect |
| 34. C2×Dic538 | C2×C4 | semidirect |
| 47. #16864379 | C2×C4 | semidirect |
| 48. #16864379 | C2×C4 | semidirect |
| 58. C42×C269 | C2×C4 | semidirect |
| 118. C269 | #2337 | semidirect |
| 127. C4×C4⋊C4 | D269 | semidirect |
| 177. C42 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575441 | 2 |
| #31770509 | 2 |
| #31770496 | 2 |
| #31770495 | 2 |
| #31770483 | 2 |
| #31770476 | 2 |
| #31770473 | 2 |
| C4×#16864379 | 2 |
| C4×C4⋊C4×C269 | 2 |
| #2337 | 269 |