Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 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×#22575484 | C2 | semidirect |
| 3. #31770997 | C2 | semidirect |
| 4. #31770984 | C2 | semidirect |
| 5. #31770979 | C2 | semidirect |
| 6. C4×#16864386 | C2 | semidirect |
| 7. C2×C4⋊Q8×C269 | C2 | semidirect |
| 34. #16864386 | D4 | semidirect |
| 76. C4×C269 | #137 | semidirect |
| 83. C269 | #3152 | semidirect |
| 87. C2×C4⋊Q8 | D269 | semidirect |
| 161. C4 | #22575484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575484 | 2 |
| #31771155 | 2 |
| #31770997 | 2 |
| #31770984 | 2 |
| #31770979 | 2 |
| C4×#16864386 | 2 |
| C2×C4⋊Q8×C269 | 2 |
| #3152 | 269 |