Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
1252 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 2. C2×#22548677 | C2 | semidirect |
| 3. C2×C22⋊C4×D251 | C2 | semidirect |
| 4. #30631588 | C2 | semidirect |
| 5. #30631565 | C2 | semidirect |
| 6. #30631542 | C2 | semidirect |
| 7. C4×C22⋊Dic251 | C2 | semidirect |
| 8. #380×C251 | C2 | semidirect |
| 11. C22×D1004 | C4 | semidirect |
| 15. C22×C4×D251 | C22 | semidirect |
| 19. C2×(C2×D251)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D251)⋊C4 | C22 | semidirect |
| 21. C2×(C2×D251)⋊C4 | C22 | semidirect |
| 23. C2×C4×Dic251 | C22 | semidirect |
| 24. C251⋊#95 | C22 | semidirect |
| 26. C2×C4⋊C4×C251 | C22 | semidirect |
| 28. #95×C251 | C22 | semidirect |
| 33. C23×D251 | C2×C4 | semidirect |
| 40. C2×D1004 | C2×C4 | semidirect |
| 41. C2×D1004 | C2×C4 | semidirect |
| 49. C22⋊Dic251 | D4 | semidirect |
| 56. C22×C4×C251 | C2×C4 | semidirect |
| 79. D1004 | C22⋊C4 | semidirect |
| 85. C2×Dic251 | C2×D4 | semidirect |
| 105. C22×C251 | C4×D4 | semidirect |
| 121. C2×D251 | C2×C22⋊C4 | semidirect |
| 124. C4×C251 | C2×C22⋊C4 | semidirect |
| 135. C251 | D4×C22⋊C4 | semidirect |
| 142. #380 | D251 | semidirect |
| 154. C2×C4⋊C4 | C2×D251 | semidirect |
| 164. #95 | C2×D251 | semidirect |
| 186. C22×C4 | C4×D251 | semidirect |
| 252. C22 | #22548677 | semidirect |
| 262. C4 | C22⋊C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D1004 | 2 |
| C2×#22548677 | 2 |
| C2×C22⋊C4×D251 | 2 |
| #30631588 | 2 |
| #30631565 | 2 |
| #30631542 | 2 |
| C4×C22⋊Dic251 | 2 |
| #380×C251 | 2 |
| D4×C22⋊C4 | 251 |