Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 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×#22575486 | C2 | semidirect |
| 2. #31771264 | C2 | semidirect |
| 3. #31770989 | C2 | semidirect |
| 4. #31770851 | C2 | semidirect |
| 5. #31770828 | C2 | semidirect |
| 6. #31770763 | C2 | semidirect |
| 7. #31770752 | C2 | semidirect |
| 8. C4×Dic1076 | C2 | semidirect |
| 9. #436×C269 | C2 | semidirect |
| 50. Dic1076 | D4 | semidirect |
| 117. C269 | #3277 | semidirect |
| 127. #436 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575486 | 2 |
| #31771264 | 2 |
| #31770989 | 2 |
| #31770851 | 2 |
| #31770828 | 2 |
| #31770763 | 2 |
| #31770752 | 2 |
| C4×Dic1076 | 2 |
| #436×C269 | 2 |
| #3277 | 269 |