Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 51 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. #31770807 | C2 | semidirect |
| 3. #31770684 | C2 | semidirect |
| 4. #31770356 | C2 | semidirect |
| 5. #31770351 | C2 | semidirect |
| 6. #31770349 | C2 | semidirect |
| 7. #486×C269 | C2 | semidirect |
| 84. C269 | #1701 | semidirect |
| 86. #486 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31770807 | 2 |
| #31770797 | 2 |
| #31770684 | 2 |
| #31770356 | 2 |
| #31770351 | 2 |
| #31770349 | 2 |
| #486×C269 | 2 |
| #1701 | 269 |