Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#22575486 | C2 | semidirect |
| 2. C2×#22575473 | C2 | semidirect |
| 3. C22×#16864390 | C2 | semidirect |
| 4. #31771176 | C2 | semidirect |
| 5. #31771172 | C2 | semidirect |
| 6. #31770996 | C2 | semidirect |
| 7. #31770993 | C2 | semidirect |
| 8. #31770988 | C2 | semidirect |
| 9. #31770976 | C2 | semidirect |
| 10. #31770563 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C269 | C2 | semidirect |
| 16. C2×Dic1076 | C22 | semidirect |
| 17. C2×#16864392 | C22 | semidirect |
| 18. C2×#16864391 | C22 | semidirect |
| 22. C2×#16864390 | C22 | semidirect |
| 23. C2×#16864389 | C22 | semidirect |
| 24. C2×#16864387 | C22 | semidirect |
| 26. #22575451 | C22 | semidirect |
| 29. #22575440 | C22 | semidirect |
| 35. #22575363 | C22 | semidirect |
| 36. C8×Dic269 | C22 | semidirect |
| 63. C2×#14524130 | D4 | semidirect |
| 86. M16×C269 | D4 | semidirect |
| 148. C269 | #3154 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D269 | semidirect |
| 226. M16 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575486 | 2 |
| C2×#22575473 | 2 |
| C22×#16864390 | 2 |
| #31771176 | 2 |
| #31771172 | 2 |
| #31770996 | 2 |
| #31770993 | 2 |
| #31770988 | 2 |
| #31770976 | 2 |
| #31770563 | 2 |
| C2×AGL(1,ℤ/8)×C269 | 2 |
| #3154 | 269 |