Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#22575452 | C2 | semidirect |
| 3. #31770899 | C2 | semidirect |
| 4. #31770894 | C2 | semidirect |
| 5. #31770889 | C2 | semidirect |
| 6. #31770884 | C2 | semidirect |
| 7. #31770648 | C2 | semidirect |
| 8. #31770628 | C2 | semidirect |
| 11. #428×C269 | C2 | semidirect |
| 44. #16864402 | Q8 | semidirect |
| 87. Dic538 | C2×Q8 | semidirect |
| 89. D1076 | C2×Q8 | semidirect |
| 138. C269 | #3079 | semidirect |
| 147. #428 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575452 | 2 |
| #31771073 | 2 |
| #31770899 | 2 |
| #31770894 | 2 |
| #31770889 | 2 |
| #31770884 | 2 |
| #31770648 | 2 |
| #31770628 | 2 |
| #31770607 | 2 |
| #31770604 | 2 |
| #428×C269 | 2 |
| #3079 | 269 |