Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#16864390 | C2 | semidirect |
| 2. #31771176 | C2 | semidirect |
| 3. #31771080 | C2 | semidirect |
| 4. #31770818 | C2 | semidirect |
| 5. #31770808 | C2 | semidirect |
| 6. #31770633 | C2 | semidirect |
| 7. #31770615 | C2 | semidirect |
| 8. #31770601 | C2 | semidirect |
| 14. #22575451 | C22 | semidirect |
| 15. #22575440 | C22 | semidirect |
| 23. #22575382 | C22 | semidirect |
| 24. #22575378 | C22 | semidirect |
| 25. #22575377 | C22 | semidirect |
| 26. #22575374 | C22 | semidirect |
| 116. C269 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864390 | 2 |
| #31771176 | 2 |
| #31771080 | 2 |
| #31770818 | 2 |
| #31770808 | 2 |
| #31770633 | 2 |
| #31770615 | 2 |
| #31770601 | 2 |
| C2×AGL(1,ℤ/8)×C269 | 2 |
| #3042 | 269 |