Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #30632234 | C2 | semidirect |
| 2. #30632091 | C2 | semidirect |
| 3. #30632062 | C2 | semidirect |
| 4. #30632032 | C2 | semidirect |
| 5. #30631924 | C2 | semidirect |
| 6. #30631922 | C2 | semidirect |
| 7. #30631920 | C2 | semidirect |
| 8. C4×D2008 | C2 | semidirect |
| 9. C4×#16860795 | C2 | semidirect |
| 10. C4×C8×D251 | C2 | semidirect |
| 11. C4×D8×C251 | C2 | semidirect |
| 89. C4×D251 | D8 | semidirect |
| 91. C251⋊C8 | #41 | semidirect |
| 101. C8×C251 | #41 | semidirect |
| 127. C251 | #3169 | semidirect |
| 138. C4×D8 | D251 | semidirect |
| 229. C8 | #16860810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632234 | 2 |
| #30632091 | 2 |
| #30632062 | 2 |
| #30632032 | 2 |
| #30631924 | 2 |
| #30631922 | 2 |
| #30631920 | 2 |
| C4×D2008 | 2 |
| C4×#16860795 | 2 |
| C4×C8×D251 | 2 |
| C4×D8×C251 | 2 |
| #3169 | 251 |