Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. C2×#22575476 | C2 | semidirect |
| 2. C2×#22575461 | C2 | semidirect |
| 3. #31771185 | C2 | semidirect |
| 4. #31770860 | C2 | semidirect |
| 5. #31770859 | C2 | semidirect |
| 6. #31770858 | C2 | semidirect |
| 7. #31770837 | C2 | semidirect |
| 8. #31770836 | C2 | semidirect |
| 9. #106×D269 | C2 | semidirect |
| 10. #31770605 | C2 | semidirect |
| 11. #470×C269 | C2 | semidirect |
| 65. C8×D269 | D4 | semidirect |
| 139. C269 | #3060 | semidirect |
| 145. #470 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575476 | 2 |
| C2×#22575461 | 2 |
| #31771185 | 2 |
| #31770860 | 2 |
| #31770859 | 2 |
| #31770858 | 2 |
| #31770837 | 2 |
| #31770836 | 2 |
| #106×D269 | 2 |
| #31770605 | 2 |
| #470×C269 | 2 |
| #3060 | 269 |