Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
356 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #31771009 | C2 | semidirect |
| 3. #31771007 | C2 | semidirect |
| 4. #31771004 | C2 | semidirect |
| 5. #31771002 | C2 | semidirect |
| 9. #499×C269 | C2 | semidirect |
| 34. C8×D269 | Q8 | semidirect |
| 35. C8×D269 | Q8 | semidirect |
| 76. C269 | #3160 | semidirect |
| 82. #499 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771161 | 2 |
| #31771009 | 2 |
| #31771007 | 2 |
| #31771004 | 2 |
| #31771002 | 2 |
| #31770642 | 2 |
| #31770640 | 2 |
| C4×C8×D269 | 2 |
| #499×C269 | 2 |
| #3160 | 269 |