Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
304 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 77 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×C22⋊#14524130 | C2 | semidirect |
| 3. #31770341 | C2 | semidirect |
| 4. #31770338 | C2 | semidirect |
| 5. C4×C22⋊C4×C269 | C2 | semidirect |
| 6. C2×#16864402 | C4 | semidirect |
| 9. #22575432 | C4 | semidirect |
| 11. #22575427 | C4 | semidirect |
| 16. #22575412 | C4 | semidirect |
| 112. C269 | #1501 | semidirect |
| 116. C4×C22⋊C4 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771116 | 2 |
| C2×C22⋊#14524130 | 2 |
| #31770341 | 2 |
| #31770338 | 2 |
| C4×C22⋊C4×C269 | 2 |
| #1501 | 269 |