Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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×#22575382 | C2 | semidirect |
| 4. C2×C4×#14524130 | C2 | semidirect |
| 6. #31770359 | C2 | semidirect |
| 7. #336×C269 | C2 | semidirect |
| 40. #16864379 | C8 | semidirect |
| 122. C269 | #1923 | semidirect |
| 130. #336 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575382 | 2 |
| C2×#22575365 | 2 |
| C2×C4×#14524130 | 2 |
| C4×#16864379 | 2 |
| #31770359 | 2 |
| #336×C269 | 2 |
| #1923 | 269 |