Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31770955 | C2 | semidirect |
| 3. #31770938 | C2 | semidirect |
| 4. #31770900 | C2 | semidirect |
| 5. #31770844 | C2 | semidirect |
| 6. #31770812 | C2 | semidirect |
| 7. #31770761 | C2 | semidirect |
| 8. C4×#16864392 | C2 | semidirect |
| 10. C2×#22575377 | C2 | semidirect |
| 92. D4×C269 | Q16 | semidirect |
| 122. C269 | #3299 | semidirect |
| 208. D4 | #16864392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771312 | 2 |
| #31770955 | 2 |
| #31770938 | 2 |
| #31770900 | 2 |
| #31770844 | 2 |
| #31770812 | 2 |
| #31770761 | 2 |
| C4×#16864392 | 2 |
| D4×#14524130 | 2 |
| C2×#22575377 | 2 |
| D4×Q8×C269 | 2 |
| #3299 | 269 |