Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22575459 | C2 | semidirect |
| 2. #31771172 | C2 | semidirect |
| 3. #31770855 | C2 | semidirect |
| 4. #31770838 | C2 | semidirect |
| 5. #31770643 | C2 | semidirect |
| 6. #31770610 | C2 | semidirect |
| 7. C22×D8×C269 | C2 | semidirect |
| 11. C2×#16864385 | C22 | semidirect |
| 12. C2×C8×D269 | C22 | semidirect |
| 15. #22575424 | C22 | semidirect |
| 18. #22575387 | C22 | semidirect |
| 19. #22575385 | C22 | semidirect |
| 20. #22575374 | C22 | semidirect |
| 49. C2×C8×C269 | D4 | semidirect |
| 93. C269 | #3058 | semidirect |
| 95. C22×D8 | D269 | semidirect |
| 139. C2×C8 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575459 | 2 |
| #31771172 | 2 |
| #31770855 | 2 |
| #31770838 | 2 |
| #31770643 | 2 |
| #31770610 | 2 |
| C22×D8×C269 | 2 |
| #3058 | 269 |