Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×D1076 | C2 | semidirect |
| 2. #31770933 | C2 | semidirect |
| 3. #31770916 | C2 | semidirect |
| 4. #31770902 | C2 | semidirect |
| 5. #31770817 | C2 | semidirect |
| 6. #31770755 | C2 | semidirect |
| 8. #31770715 | C2 | semidirect |
| 9. #31770703 | C2 | semidirect |
| 10. #31770662 | C2 | semidirect |
| 11. #529×C269 | C2 | semidirect |
| 22. #22575386 | C22 | semidirect |
| 23. #22575384 | C22 | semidirect |
| 24. C4⋊#14524130 | C22 | semidirect |
| 25. #22575377 | C22 | semidirect |
| 26. #22575374 | C22 | semidirect |
| 31. #22575364 | C22 | semidirect |
| 33. #125×C269 | C22 | semidirect |
| 34. #124×C269 | C22 | semidirect |
| 38. C4×Q8×C269 | C22 | semidirect |
| 40. C4×D4×C269 | C22 | semidirect |
| 140. C269 | #3114 | semidirect |
| 142. #529 | D269 | semidirect |
| 158. #125 | C2×D269 | semidirect |
| 159. #124 | C2×D269 | semidirect |
| 163. C4×Q8 | C2×D269 | semidirect |
| 169. C4×D4 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1076 | 2 |
| #31770933 | 2 |
| #31770916 | 2 |
| #31770902 | 2 |
| #31770817 | 2 |
| #31770755 | 2 |
| #31770738 | 2 |
| #31770715 | 2 |
| #31770703 | 2 |
| #31770662 | 2 |
| #529×C269 | 2 |
| #3114 | 269 |