Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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. C22×C8×D251 | C2 | semidirect |
| 3. #30632199 | C2 | semidirect |
| 4. #30631929 | C2 | semidirect |
| 5. #30631924 | C2 | semidirect |
| 6. #30631917 | C2 | semidirect |
| 7. #30631681 | C2 | semidirect |
| 8. #427×C251 | C2 | semidirect |
| 12. C2×Dic1004 | C22 | semidirect |
| 13. C2×#16860799 | C22 | semidirect |
| 14. C2×D2008 | C22 | semidirect |
| 24. #22548638 | C22 | semidirect |
| 25. #22548635 | C22 | semidirect |
| 28. #107×C251 | C22 | semidirect |
| 29. #106×C251 | C22 | semidirect |
| 54. C2×C8×C251 | D4 | semidirect |
| 94. C2×D251 | #135 | semidirect |
| 106. C251 | #3050 | semidirect |
| 114. #427 | D251 | semidirect |
| 133. #107 | C2×D251 | semidirect |
| 134. #106 | C2×D251 | semidirect |
| 158. C2×C8 | D1004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548737 | 2 |
| C22×C8×D251 | 2 |
| #30632199 | 2 |
| #30631929 | 2 |
| #30631924 | 2 |
| #30631917 | 2 |
| #30631681 | 2 |
| #427×C251 | 2 |
| #3050 | 251 |