Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 3. #31771013 | C2 | semidirect |
| 4. #31771012 | C2 | semidirect |
| 5. #31771006 | C2 | semidirect |
| 6. #31771005 | C2 | semidirect |
| 48. #16864386 | Q8 | semidirect |
| 72. M16×C269 | Q8 | semidirect |
| 124. C269 | #3166 | semidirect |
| 176. M16 | Dic538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771158 | 2 |
| C2×#22575444 | 2 |
| #31771013 | 2 |
| #31771012 | 2 |
| #31771006 | 2 |
| #31771005 | 2 |
| #31770648 | 2 |
| #31770647 | 2 |
| #31770645 | 2 |
| M16×Dic269 | 2 |
| #428×C269 | 2 |
| #3166 | 269 |