Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31770967 | C2 | semidirect |
| 3. #31770962 | C2 | semidirect |
| 4. #31770613 | C2 | semidirect |
| 6. C4×#16864386 | C2 | semidirect |
| 7. #533×C269 | C2 | semidirect |
| 15. #22575376 | C22 | semidirect |
| 17. #22575364 | C22 | semidirect |
| 18. C4×#14524130 | C22 | semidirect |
| 19. C4⋊Q8×C269 | C22 | semidirect |
| 20. #125×C269 | C22 | semidirect |
| 83. C269 | #3140 | semidirect |
| 85. #533 | D269 | semidirect |
| 95. C4⋊Q8 | C2×D269 | semidirect |
| 96. #125 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575441 | 2 |
| #31770967 | 2 |
| #31770962 | 2 |
| #31770613 | 2 |
| #31770609 | 2 |
| C4×#16864386 | 2 |
| #533×C269 | 2 |
| #3140 | 269 |