Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 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. #31771316 | C2 | semidirect |
| 3. #31770922 | C2 | semidirect |
| 4. #31770892 | C2 | semidirect |
| 5. #31770833 | C2 | semidirect |
| 6. #31770802 | C2 | semidirect |
| 7. #31770757 | C2 | semidirect |
| 8. C4×#16864391 | C2 | semidirect |
| 9. C8×D1076 | C2 | semidirect |
| 10. #102×D269 | C2 | semidirect |
| 11. #486×C269 | C2 | semidirect |
| 15. C2×#16864390 | C22 | semidirect |
| 16. C2×C8×D269 | C22 | semidirect |
| 18. #22575433 | C22 | semidirect |
| 23. C4×Dic538 | C22 | semidirect |
| 27. C4⋊C4×D269 | C22 | semidirect |
| 28. #22575385 | C22 | semidirect |
| 29. #22575384 | C22 | semidirect |
| 30. C4⋊#14524130 | C22 | semidirect |
| 31. #22575378 | C22 | semidirect |
| 33. #22575374 | C22 | semidirect |
| 35. #22575365 | C22 | semidirect |
| 36. C4⋊Q8×C269 | C22 | semidirect |
| 38. #102×C269 | C22 | semidirect |
| 39. #102×C269 | C22 | semidirect |
| 40. C4×C8×C269 | C22 | semidirect |
| 85. D1076 | SD16 | semidirect |
| 136. C269 | #3295 | semidirect |
| 140. #486 | D269 | semidirect |
| 154. C4⋊Q8 | C2×D269 | semidirect |
| 174. #102 | C2×D269 | semidirect |
| 175. #102 | C2×D269 | semidirect |
| 177. C4×C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771316 | 2 |
| #31771240 | 2 |
| #31770922 | 2 |
| #31770892 | 2 |
| #31770833 | 2 |
| #31770802 | 2 |
| #31770757 | 2 |
| C4×#16864391 | 2 |
| C8×D1076 | 2 |
| #102×D269 | 2 |
| #486×C269 | 2 |
| #3295 | 269 |