Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
376 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 143 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. #31770914 | C2 | semidirect |
| 4. #31770910 | C2 | semidirect |
| 5. #31770898 | C2 | semidirect |
| 6. #31770888 | C2 | semidirect |
| 72. C2×Q8×C269 | Q8 | semidirect |
| 129. C269 | #3078 | semidirect |
| 177. C2×Q8 | Dic538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771158 | 2 |
| C2×Q8×Dic269 | 2 |
| #31770914 | 2 |
| #31770910 | 2 |
| #31770898 | 2 |
| #31770888 | 2 |
| #31770648 | 2 |
| #31770647 | 2 |
| #31770628 | 2 |
| #31770614 | 2 |
| #419×C269 | 2 |
| #3078 | 269 |