Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31771162 | C2 | semidirect |
| 2. #31770964 | C2 | semidirect |
| 3. #31770959 | C2 | semidirect |
| 4. #31770614 | C2 | semidirect |
| 6. C4×#16864386 | C2 | semidirect |
| 9. #22575453 | C22 | semidirect |
| 10. #22575445 | C22 | semidirect |
| 14. #22575377 | C22 | semidirect |
| 16. #22575364 | C22 | semidirect |
| 17. C4×#14524130 | C22 | semidirect |
| 83. C269 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771162 | 2 |
| #31770964 | 2 |
| #31770959 | 2 |
| #31770614 | 2 |
| #31770610 | 2 |
| C4×#16864386 | 2 |
| C2×#124×C269 | 2 |
| #3140 | 269 |