Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
362 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 2. #31770912 | C2 | semidirect |
| 3. #31770912 | C2 | semidirect |
| 4. #31770900 | C2 | semidirect |
| 5. #31770890 | C2 | semidirect |
| 59. C2×Q8×C269 | Q8 | semidirect |
| 116. C269 | #3082 | semidirect |
| 161. C2×Q8 | Dic538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771233 | 2 |
| #31770912 | 2 |
| #31770900 | 2 |
| #31770890 | 2 |
| #31770648 | 2 |
| #31770641 | 2 |
| #31770632 | 2 |
| #31770614 | 2 |
| C2×#22575377 | 2 |
| #519×C269 | 2 |
| #3082 | 269 |