Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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. #31771007 | C2 | semidirect |
| 3. #31770428 | C2 | semidirect |
| 5. #364×C269 | C2 | semidirect |
| 50. C269 | #2231 | semidirect |
| 55. #364 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771007 | 2 |
| #31770723 | 2 |
| #31770428 | 2 |
| #31770416 | 2 |
| #364×C269 | 2 |
| #2231 | 269 |