Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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. C2×#22575479 | C2 | semidirect |
| 2. C2×#22575475 | C2 | semidirect |
| 3. #31771172 | C2 | semidirect |
| 4. #31770993 | C2 | semidirect |
| 5. #31770988 | C2 | semidirect |
| 6. #31770980 | C2 | semidirect |
| 7. #31770560 | C2 | semidirect |
| 8. C22×D8×C269 | C2 | semidirect |
| 12. C2×Dic1076 | C22 | semidirect |
| 13. C2×#16864391 | C22 | semidirect |
| 14. C2×#16864390 | C22 | semidirect |
| 15. C2×D2152 | C22 | semidirect |
| 16. C2×#16864387 | C22 | semidirect |
| 18. #22575449 | C22 | semidirect |
| 19. #22575440 | C22 | semidirect |
| 23. #22575363 | C22 | semidirect |
| 24. C8×Dic269 | C22 | semidirect |
| 42. #16864386 | D4 | semidirect |
| 56. C2×C8×C269 | D4 | semidirect |
| 101. C269 | #3155 | semidirect |
| 105. C22×D8 | D269 | semidirect |
| 154. 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×#22575479 | 2 |
| C2×#22575475 | 2 |
| #31771172 | 2 |
| #31770993 | 2 |
| #31770988 | 2 |
| #31770980 | 2 |
| #31770560 | 2 |
| C22×D8×C269 | 2 |
| #3155 | 269 |