Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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. #31770653 | C2 | semidirect |
| 2. #31770631 | C2 | semidirect |
| 6. #31770361 | C2 | semidirect |
| 7. #424×C269 | C2 | semidirect |
| 89. C269 | #2098 | semidirect |
| 93. #424 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31770653 | 2 |
| #31770631 | 2 |
| #31770623 | 2 |
| #31770621 | 2 |
| #31770571 | 2 |
| #31770361 | 2 |
| #424×C269 | 2 |
| #2098 | 269 |