Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #31771325 | C2 | semidirect |
| 2. #31770952 | C2 | semidirect |
| 3. #31770806 | C2 | semidirect |
| 5. #31770350 | C2 | semidirect |
| 6. #31770337 | C2 | semidirect |
| 7. D4⋊C8×C269 | C2 | semidirect |
| 95. C269 | #1628 | semidirect |
| 103. D4⋊C8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771325 | 2 |
| #31770952 | 2 |
| #31770806 | 2 |
| #31770800 | 2 |
| #31770350 | 2 |
| #31770337 | 2 |
| D4⋊C8×C269 | 2 |
| #1628 | 269 |