Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
380 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 4. #31770889 | C2 | semidirect |
| 5. #31770814 | C2 | semidirect |
| 8. #31770711 | C2 | semidirect |
| 9. #31770709 | C2 | semidirect |
| 127. C269 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771157 | 2 |
| C2×#22575418 | 2 |
| #31770935 | 2 |
| #31770889 | 2 |
| #31770814 | 2 |
| #31770763 | 2 |
| #31770760 | 2 |
| #31770711 | 2 |
| #31770709 | 2 |
| #31770659 | 2 |
| #483×C269 | 2 |
| #3113 | 269 |