Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #31771083 | C2 | semidirect |
| 4. #31770708 | C2 | semidirect |
| 5. #31770690 | C2 | semidirect |
| 6. #31770641 | C2 | semidirect |
| 8. #31770563 | C2 | semidirect |
| 9. #419×C269 | C2 | semidirect |
| 11. C2×#16864389 | C4 | semidirect |
| 16. Q8×Dic269 | C22 | semidirect |
| 23. #22575386 | C22 | semidirect |
| 24. #22575384 | C22 | semidirect |
| 26. #22575363 | C22 | semidirect |
| 27. C8×Dic269 | C22 | semidirect |
| 31. #103×C269 | C22 | semidirect |
| 38. #16864389 | C2×C4 | semidirect |
| 39. #16864389 | C2×C4 | semidirect |
| 40. C2×#14524130 | C2×C4 | semidirect |
| 54. C2×Q8×C269 | C2×C4 | semidirect |
| 103. C269 | #2949 | semidirect |
| 111. #419 | D269 | semidirect |
| 132. #103 | C2×D269 | semidirect |
| 139. C2×Q8 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864389 | 2 |
| #31771083 | 2 |
| #31771079 | 2 |
| #31770708 | 2 |
| #31770690 | 2 |
| #31770641 | 2 |
| #31770611 | 2 |
| #31770563 | 2 |
| #419×C269 | 2 |
| #2949 | 269 |