Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
644 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
|---|---|---|
| 3. #31770512 | C2 | semidirect |
| 4. #31770501 | C2 | semidirect |
| 5. #31770475 | C2 | semidirect |
| 7. C2×C4⋊Q8×C269 | C2 | semidirect |
| 32. C2×C4×D269 | Q8 | semidirect |
| 82. C2×D269 | C4⋊Q8 | semidirect |
| 85. C4×C269 | C22⋊Q8 | semidirect |
| 95. C269 | #2857 | semidirect |
| 97. C2×C4⋊Q8 | D269 | semidirect |
| 184. C4 | #22575429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575429 | 2 |
| C2×C42×D269 | 2 |
| #31770512 | 2 |
| #31770501 | 2 |
| #31770475 | 2 |
| #31770462 | 2 |
| C2×C4⋊Q8×C269 | 2 |
| #2857 | 269 |