Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 482 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. C2×#22548737 | C2 | semidirect |
| 2. C2×Q16×D251 | C2 | semidirect |
| 3. #30632347 | C2 | semidirect |
| 4. #30632072 | C2 | semidirect |
| 5. #30631924 | C2 | semidirect |
| 6. #30631912 | C2 | semidirect |
| 7. #30631847 | C2 | semidirect |
| 8. #30631827 | C2 | semidirect |
| 9. #30631781 | C2 | semidirect |
| 10. C8×C22⋊D251 | C2 | semidirect |
| 11. #467×C251 | C2 | semidirect |
| 54. Dic1004 | D4 | semidirect |
| 120. C2×D251 | #135 | semidirect |
| 136. C251 | #3285 | semidirect |
| 142. #467 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548737 | 2 |
| C2×Q16×D251 | 2 |
| #30632347 | 2 |
| #30632072 | 2 |
| #30631924 | 2 |
| #30631912 | 2 |
| #30631847 | 2 |
| #30631827 | 2 |
| #30631781 | 2 |
| C8×C22⋊D251 | 2 |
| #467×C251 | 2 |
| #3285 | 251 |