Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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. #31770615 | C2 | semidirect |
| 4. C2×#22575371 | C2 | semidirect |
| 6. #31770560 | C2 | semidirect |
| 7. C2×#108×C269 | C2 | semidirect |
| 13. C2×#16864391 | C4 | semidirect |
| 106. C269 | #1977 | semidirect |
| 109. C2×#108 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864391 | 2 |
| #31770615 | 2 |
| #31770611 | 2 |
| C2×#22575371 | 2 |
| C2×#22575369 | 2 |
| #31770560 | 2 |
| C2×#108×C269 | 2 |
| #1977 | 269 |