Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 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. #31771372 | C2 | semidirect |
| 2. #31770727 | C2 | semidirect |
| 3. #31770722 | C2 | semidirect |
| 4. #31770654 | C2 | semidirect |
| 5. C2×#22575380 | C2 | semidirect |
| 6. M16×Dic269 | C2 | semidirect |
| 9. #22575460 | C22 | semidirect |
| 14. #22575389 | C22 | semidirect |
| 15. #22575380 | C22 | semidirect |
| 16. #22575380 | C22 | semidirect |
| 17. #22575363 | C22 | semidirect |
| 18. C8×Dic269 | C22 | semidirect |
| 20. #137×C269 | C4 | semidirect |
| 21. AGL(1,ℤ/8)×C269 | C4 | semidirect |
| 44. Q16×C269 | C2×C4 | semidirect |
| 45. SD16×C269 | C2×C4 | semidirect |
| 46. D8×C269 | C2×C4 | semidirect |
| 85. C269 | #2956 | semidirect |
| 95. #137 | Dic269 | semidirect |
| 96. AGL(1,ℤ/8) | Dic269 | semidirect |
| 120. Q16 | C2×Dic269 | semidirect |
| 121. SD16 | C2×Dic269 | semidirect |
| 122. D8 | C2×Dic269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771372 | 2 |
| #31770727 | 2 |
| #31770722 | 2 |
| #31770654 | 2 |
| C2×#22575380 | 2 |
| M16×Dic269 | 2 |
| #575×C269 | 2 |
| #2956 | 269 |