Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31771260 | C2 | semidirect |
| 2. #31771240 | C2 | semidirect |
| 3. #31770951 | C2 | semidirect |
| 4. #31770917 | C2 | semidirect |
| 5. #31770886 | C2 | semidirect |
| 6. #31770838 | C2 | semidirect |
| 7. #31770737 | C2 | semidirect |
| 8. C4×#16864387 | C2 | semidirect |
| 9. #31770670 | C2 | semidirect |
| 10. #102×D269 | C2 | semidirect |
| 11. #459×C269 | C2 | semidirect |
| 16. C2×C8×D269 | C22 | semidirect |
| 17. #22575453 | C22 | semidirect |
| 22. #22575424 | C22 | semidirect |
| 26. C4⋊C4×D269 | C22 | semidirect |
| 27. #22575387 | C22 | semidirect |
| 28. #22575386 | C22 | semidirect |
| 30. #22575374 | C22 | semidirect |
| 31. #22575374 | C22 | semidirect |
| 32. #22575374 | C22 | semidirect |
| 34. #22575365 | C22 | semidirect |
| 35. C4×#14524130 | C22 | semidirect |
| 36. C2×D8×C269 | C22 | semidirect |
| 38. C4×D4×C269 | C22 | semidirect |
| 39. C4⋊C8×C269 | C22 | semidirect |
| 40. #102×C269 | C22 | semidirect |
| 85. D1076 | D8 | semidirect |
| 86. D1076 | #41 | semidirect |
| 142. C269 | #3294 | semidirect |
| 150. #459 | D269 | semidirect |
| 159. C2×D8 | C2×D269 | semidirect |
| 171. C4×D4 | C2×D269 | semidirect |
| 175. C4⋊C8 | C2×D269 | semidirect |
| 181. #102 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771260 | 2 |
| #31771240 | 2 |
| #31770951 | 2 |
| #31770917 | 2 |
| #31770886 | 2 |
| #31770838 | 2 |
| #31770737 | 2 |
| C4×#16864387 | 2 |
| #31770670 | 2 |
| #102×D269 | 2 |
| #459×C269 | 2 |
| #3294 | 269 |