Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
376 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 135 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. #31770915 | C2 | semidirect |
| 4. #31770911 | C2 | semidirect |
| 5. #31770899 | C2 | semidirect |
| 6. #31770889 | C2 | semidirect |
| 47. C2×Dic538 | Q8 | semidirect |
| 129. C269 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771158 | 2 |
| C2×#22575418 | 2 |
| #31770915 | 2 |
| #31770911 | 2 |
| #31770899 | 2 |
| #31770889 | 2 |
| #31770645 | 2 |
| #31770628 | 2 |
| #31770615 | 2 |
| #31770613 | 2 |
| #428×C269 | 2 |
| #3078 | 269 |