Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#22575485 | C2 | semidirect |
| 2. C2×#22575480 | C2 | semidirect |
| 3. #31771156 | C2 | semidirect |
| 4. #124×D269 | C2 | semidirect |
| 5. #31770997 | C2 | semidirect |
| 6. #31770995 | C2 | semidirect |
| 7. #31770994 | C2 | semidirect |
| 8. #31770990 | C2 | semidirect |
| 9. #31770986 | C2 | semidirect |
| 10. #31770557 | C2 | semidirect |
| 11. #497×C269 | C2 | semidirect |
| 17. C2×#16864392 | C22 | semidirect |
| 18. C2×#16864391 | C22 | semidirect |
| 20. C2×#16864389 | C22 | semidirect |
| 24. #22575450 | C22 | semidirect |
| 26. #22575442 | C22 | semidirect |
| 34. #22575364 | C22 | semidirect |
| 35. C8×Dic269 | C22 | semidirect |
| 36. C2×Q16×C269 | C22 | semidirect |
| 38. C4⋊Q8×C269 | C22 | semidirect |
| 40. #97×C269 | C22 | semidirect |
| 63. #16864385 | D4 | semidirect |
| 134. C269 | #3153 | semidirect |
| 141. #497 | D269 | semidirect |
| 153. C2×Q16 | C2×D269 | semidirect |
| 161. C4⋊Q8 | C2×D269 | semidirect |
| 174. #97 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575485 | 2 |
| C2×#22575480 | 2 |
| #31771156 | 2 |
| #124×D269 | 2 |
| #31770997 | 2 |
| #31770995 | 2 |
| #31770994 | 2 |
| #31770990 | 2 |
| #31770986 | 2 |
| #31770557 | 2 |
| #497×C269 | 2 |
| #3153 | 269 |