Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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×#22575482 | C2 | semidirect |
| 3. #31771270 | C2 | semidirect |
| 4. #31770848 | C2 | semidirect |
| 5. #31770812 | C2 | semidirect |
| 6. #31770802 | C2 | semidirect |
| 7. #31770764 | C2 | semidirect |
| 8. #31770742 | C2 | semidirect |
| 9. C4×Dic1076 | C2 | semidirect |
| 10. #31770684 | C2 | semidirect |
| 11. #492×C269 | C2 | semidirect |
| 55. Dic1076 | D4 | semidirect |
| 123. C4×C269 | #137 | semidirect |
| 136. C269 | #3278 | semidirect |
| 141. #492 | D269 | semidirect |
| 265. C4 | #22575482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575482 | 2 |
| #31771275 | 2 |
| #31771270 | 2 |
| #31770848 | 2 |
| #31770812 | 2 |
| #31770802 | 2 |
| #31770764 | 2 |
| #31770742 | 2 |
| C4×Dic1076 | 2 |
| #31770684 | 2 |
| #492×C269 | 2 |
| #3278 | 269 |