Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31771210 | C2 | semidirect |
| 2. #31770905 | C2 | semidirect |
| 3. #31770902 | C2 | semidirect |
| 4. #31770856 | C2 | semidirect |
| 5. #31770839 | C2 | semidirect |
| 6. #31770800 | C2 | semidirect |
| 7. #31770797 | C2 | semidirect |
| 8. #31770632 | C2 | semidirect |
| 9. #540×C269 | C2 | semidirect |
| 106. C269 | #3259 | semidirect |
| 109. #540 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771210 | 2 |
| #31770905 | 2 |
| #31770902 | 2 |
| #31770856 | 2 |
| #31770839 | 2 |
| #31770800 | 2 |
| #31770797 | 2 |
| #31770632 | 2 |
| #540×C269 | 2 |
| #3259 | 269 |