Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
480 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 149 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. #31770812 | C2 | semidirect |
| 4. #31770807 | C2 | semidirect |
| 5. #31770629 | C2 | semidirect |
| 6. #31770614 | C2 | semidirect |
| 7. C2×C4⋊Q8×C269 | C2 | semidirect |
| 88. C4×C269 | #137 | semidirect |
| 97. C269 | #3039 | semidirect |
| 100. C2×C4⋊Q8 | D269 | semidirect |
| 188. 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 |
| C4×#16864402 | 2 |
| #31770812 | 2 |
| #31770807 | 2 |
| #31770629 | 2 |
| #31770614 | 2 |
| C2×C4⋊Q8×C269 | 2 |
| #3039 | 269 |