Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 1. C22×#16864391 | C2 | semidirect |
| 2. #31771176 | C2 | semidirect |
| 4. #31770851 | C2 | semidirect |
| 5. #31770834 | C2 | semidirect |
| 6. #31770643 | C2 | semidirect |
| 7. #31770615 | C2 | semidirect |
| 8. #31770611 | C2 | semidirect |
| 9. C2×#131×C269 | C2 | semidirect |
| 20. #22575432 | C22 | semidirect |
| 25. #22575387 | C22 | semidirect |
| 26. #22575385 | C22 | semidirect |
| 27. #22575378 | C22 | semidirect |
| 32. C2×M16×C269 | C22 | semidirect |
| 34. C22×C8×C269 | C22 | semidirect |
| 67. C2×C8×C269 | D4 | semidirect |
| 120. C269 | #3057 | semidirect |
| 123. C2×#131 | D269 | semidirect |
| 139. C2×M16 | C2×D269 | semidirect |
| 141. C22×C8 | C2×D269 | semidirect |
| 179. C2×C8 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864391 | 2 |
| #31771176 | 2 |
| #31771169 | 2 |
| #31770851 | 2 |
| #31770834 | 2 |
| #31770643 | 2 |
| #31770615 | 2 |
| #31770611 | 2 |
| C2×#131×C269 | 2 |
| #3057 | 269 |