Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#22575479 | C2 | semidirect |
| 2. #31771155 | C2 | semidirect |
| 3. #31770992 | C2 | semidirect |
| 4. #31770981 | C2 | semidirect |
| 5. #31770977 | C2 | semidirect |
| 6. C4×#16864386 | C2 | semidirect |
| 7. C2×#127×C269 | C2 | semidirect |
| 10. C2×#16864390 | C22 | semidirect |
| 11. C2×#16864387 | C22 | semidirect |
| 13. #22575453 | C22 | semidirect |
| 14. #22575450 | C22 | semidirect |
| 15. #22575441 | C22 | semidirect |
| 18. #22575364 | C22 | semidirect |
| 19. C4×#14524130 | C22 | semidirect |
| 34. #16864386 | D4 | semidirect |
| 57. #14524130 | C2×D4 | semidirect |
| 82. C4×C269 | AGL(1,ℤ/8) | semidirect |
| 90. C269 | #3151 | semidirect |
| 94. C2×#127 | D269 | semidirect |
| 174. C4 | #22575479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575479 | 2 |
| #31771155 | 2 |
| #31770992 | 2 |
| #31770981 | 2 |
| #31770977 | 2 |
| C4×#16864386 | 2 |
| C2×#127×C269 | 2 |
| #3151 | 269 |