Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22575477 | C2 | semidirect |
| 2. #31771153 | C2 | semidirect |
| 3. #127×D269 | C2 | semidirect |
| 4. #31770993 | C2 | semidirect |
| 5. #31770981 | C2 | semidirect |
| 6. #31770978 | C2 | semidirect |
| 7. #31770977 | C2 | semidirect |
| 8. C4×#16864385 | C2 | semidirect |
| 9. #493×C269 | C2 | semidirect |
| 14. C2×#16864391 | C22 | semidirect |
| 15. C2×#16864390 | C22 | semidirect |
| 16. C2×#16864387 | C22 | semidirect |
| 18. #22575453 | C22 | semidirect |
| 22. #22575440 | C22 | semidirect |
| 26. #22575363 | C22 | semidirect |
| 27. C4×#14524130 | C22 | semidirect |
| 28. C2×D8×C269 | C22 | semidirect |
| 30. #127×C269 | C22 | semidirect |
| 31. C4×C8×C269 | C22 | semidirect |
| 48. #16864385 | D4 | semidirect |
| 77. #14524130 | C2×D4 | semidirect |
| 86. C8×C269 | C2×D4 | semidirect |
| 97. C4×C269 | AGL(1,ℤ/8) | semidirect |
| 108. C269 | #3151 | semidirect |
| 115. #493 | D269 | semidirect |
| 126. C2×D8 | C2×D269 | semidirect |
| 133. #127 | C2×D269 | semidirect |
| 140. C4×C8 | C2×D269 | semidirect |
| 195. C8 | D4×D269 | semidirect |
| 209. C4 | #22575477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575477 | 2 |
| #31771153 | 2 |
| #127×D269 | 2 |
| #31770993 | 2 |
| #31770981 | 2 |
| #31770978 | 2 |
| #31770977 | 2 |
| C4×#16864385 | 2 |
| #493×C269 | 2 |
| #3151 | 269 |