Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#16864392 | C2 | semidirect |
| 3. #31770984 | C2 | semidirect |
| 4. #31770844 | C2 | semidirect |
| 5. #31770815 | C2 | semidirect |
| 6. #31770812 | C2 | semidirect |
| 7. #31770761 | C2 | semidirect |
| 8. #31770760 | C2 | semidirect |
| 9. C4×#16864392 | C2 | semidirect |
| 52. #16864392 | D4 | direct (N × H) |
| 100. D4×C269 | Q16 | semidirect |
| 113. C22×C269 | C2×Q16 | semidirect |
| 120. C4×C269 | C2×Q16 | semidirect |
| 130. C269 | D4×Q16 | semidirect |
| 224. D4 | #16864392 | direct (N × H) |
| 244. C22 | C2×#16864392 | semidirect |
| 254. C4 | C2×#16864392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864392 | 2 |
| D4×Dic538 | 2 |
| #31770984 | 2 |
| #31770844 | 2 |
| #31770815 | 2 |
| #31770812 | 2 |
| #31770761 | 2 |
| #31770760 | 2 |
| C4×#16864392 | 2 |
| D4×#14524130 | 2 |
| D4×Q8×C269 | 2 |
| D4×Q16 | 269 |