Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 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. #31770909 | C2 | semidirect |
| 3. #31770902 | C2 | semidirect |
| 4. #31770645 | C2 | semidirect |
| 5. #31770629 | C2 | semidirect |
| 7. C2×#125×C269 | C2 | semidirect |
| 90. C269 | #3080 | semidirect |
| 92. C2×#125 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864402 | 2 |
| #31770909 | 2 |
| #31770902 | 2 |
| #31770645 | 2 |
| #31770629 | 2 |
| #31770604 | 2 |
| C2×#125×C269 | 2 |
| #3080 | 269 |