Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#22575377 | C2 | semidirect |
| 5. C2×#22575363 | C2 | semidirect |
| 6. #31770474 | C2 | semidirect |
| 7. C2×#103×C269 | C2 | semidirect |
| 11. #22575442 | C4 | semidirect |
| 112. C269 | #1959 | semidirect |
| 116. C2×#103 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575442 | 2 |
| C2×#22575377 | 2 |
| C2×#22575375 | 2 |
| C2×#22575373 | 2 |
| C2×#22575363 | 2 |
| #31770474 | 2 |
| C2×#103×C269 | 2 |
| #1959 | 269 |