Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31771371 | C2 | semidirect |
| 3. #31770621 | C2 | semidirect |
| 4. #31770611 | C2 | semidirect |
| 5. C2×#22575369 | C2 | semidirect |
| 6. #31770376 | C2 | semidirect |
| 7. #338×C269 | C2 | semidirect |
| 12. C2×#16864391 | C4 | semidirect |
| 13. C2×D2152 | C4 | semidirect |
| 112. C269 | #1903 | semidirect |
| 120. #338 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575481 | 2 |
| #31771371 | 2 |
| #31770621 | 2 |
| #31770611 | 2 |
| C2×#22575369 | 2 |
| #31770376 | 2 |
| #338×C269 | 2 |
| #1903 | 269 |