Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
456 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 181 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. #31770709 | C2 | semidirect |
| 5. #31770697 | C2 | semidirect |
| 11. C2×#16864392 | C4 | semidirect |
| 98. C269 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864392 | 2 |
| #31771083 | 2 |
| #31771082 | 2 |
| #31770709 | 2 |
| #31770697 | 2 |
| #31770641 | 2 |
| #31770615 | 2 |
| #31770563 | 2 |
| #419×C269 | 2 |
| #2950 | 269 |