Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31771329 | C2 | semidirect |
| 3. #31771008 | C2 | semidirect |
| 4. #31770942 | C2 | semidirect |
| 5. #31770928 | C2 | semidirect |
| 6. #31770891 | C2 | semidirect |
| 7. #31770850 | C2 | semidirect |
| 8. C4×#16864390 | C2 | semidirect |
| 9. #31770682 | C2 | semidirect |
| 10. #31770646 | C2 | semidirect |
| 11. #474×C269 | C2 | semidirect |
| 88. #14524130 | #41 | semidirect |
| 122. C269 | #3353 | semidirect |
| 130. #474 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771329 | 2 |
| #31771260 | 2 |
| #31771008 | 2 |
| #31770942 | 2 |
| #31770928 | 2 |
| #31770891 | 2 |
| #31770850 | 2 |
| C4×#16864390 | 2 |
| #31770682 | 2 |
| #31770646 | 2 |
| #474×C269 | 2 |
| #3353 | 269 |