Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31771330 | C2 | semidirect |
| 3. #31770972 | C2 | semidirect |
| 4. #31770910 | C2 | semidirect |
| 5. #31770897 | C2 | semidirect |
| 8. #31770735 | C2 | semidirect |
| 11. #487×C269 | C2 | semidirect |
| 116. C269 | #3372 | semidirect |
| 121. #487 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771330 | 2 |
| #31771316 | 2 |
| #31770972 | 2 |
| #31770910 | 2 |
| #31770897 | 2 |
| #31770809 | 2 |
| #31770807 | 2 |
| #31770735 | 2 |
| #31770708 | 2 |
| C4×#16864391 | 2 |
| #487×C269 | 2 |
| #3372 | 269 |