Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #30632235 | C2 | semidirect |
| 2. C4×#16860811 | C2 | semidirect |
| 3. #30632009 | C2 | semidirect |
| 4. #30631972 | C2 | semidirect |
| 5. #30631968 | C2 | semidirect |
| 6. #30631879 | C2 | semidirect |
| 7. #30631831 | C2 | semidirect |
| 8. #30631796 | C2 | semidirect |
| 9. #30631788 | C2 | semidirect |
| 10. #30631743 | C2 | semidirect |
| 11. #460×C251 | C2 | semidirect |
| 88. D1004 | #41 | semidirect |
| 106. Q8×C251 | #41 | semidirect |
| 144. C251 | #3115 | semidirect |
| 151. #460 | D251 | semidirect |
| 233. Q8 | #16860809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632235 | 2 |
| C4×#16860811 | 2 |
| #30632009 | 2 |
| #30631972 | 2 |
| #30631968 | 2 |
| #30631879 | 2 |
| #30631831 | 2 |
| #30631796 | 2 |
| #30631788 | 2 |
| #30631743 | 2 |
| #460×C251 | 2 |
| #3115 | 251 |