Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 1. C2×#22575388 | C2 | semidirect |
| 5. #31770364 | C2 | semidirect |
| 6. #31770359 | C2 | semidirect |
| 7. #405×C269 | C2 | semidirect |
| 14. #22575376 | C4 | semidirect |
| 15. #22575376 | C4 | semidirect |
| 16. #22575373 | C4 | semidirect |
| 17. #22575373 | C4 | semidirect |
| 105. C269 | #1929 | semidirect |
| 111. #405 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575388 | 2 |
| C2×#22575379 | 2 |
| #31770599 | 2 |
| #31770571 | 2 |
| #31770364 | 2 |
| #31770359 | 2 |
| #405×C269 | 2 |
| #1929 | 269 |