Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #31770956 | C2 | semidirect |
| 4. #31770941 | C2 | semidirect |
| 5. #31770901 | C2 | semidirect |
| 6. #31770846 | C2 | semidirect |
| 7. #31770816 | C2 | semidirect |
| 8. #31770763 | C2 | semidirect |
| 9. C4×Dic1076 | C2 | semidirect |
| 10. C2×#22575378 | C2 | semidirect |
| 93. D4×C269 | Q16 | semidirect |
| 122. C269 | #3299 | semidirect |
| 208. D4 | Dic1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771312 | 2 |
| D4×Dic538 | 2 |
| #31770956 | 2 |
| #31770941 | 2 |
| #31770901 | 2 |
| #31770846 | 2 |
| #31770816 | 2 |
| #31770763 | 2 |
| C4×Dic1076 | 2 |
| C2×#22575378 | 2 |
| C8×D4×C269 | 2 |
| #3299 | 269 |