Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 340 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. #31771334 | C2 | semidirect |
| 2. #31770975 | C2 | semidirect |
| 3. #31770957 | C2 | semidirect |
| 4. #31770909 | C2 | semidirect |
| 5. #31770897 | C2 | semidirect |
| 8. #31770736 | C2 | semidirect |
| 116. C269 | #3372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771334 | 2 |
| #31770975 | 2 |
| #31770957 | 2 |
| #31770909 | 2 |
| #31770897 | 2 |
| #31770810 | 2 |
| #31770736 | 2 |
| #31770705 | 2 |
| C4×#16864390 | 2 |
| #554×C269 | 2 |
| #3372 | 269 |