Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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. C4×D2008 | C2 | semidirect |
| 3. #30631514 | C2 | semidirect |
| 4. #30631488 | C2 | semidirect |
| 5. #30631487 | C2 | semidirect |
| 6. #30631463 | C2 | semidirect |
| 7. C4×D8×C251 | C2 | semidirect |
| 10. #22548656 | C4 | semidirect |
| 23. D2008 | C2×C4 | semidirect |
| 27. C251⋊C16 | C2×C4 | semidirect |
| 31. D8×C251 | C2×C4 | semidirect |
| 71. C251 | #2177 | semidirect |
| 75. C4×D8 | D251 | semidirect |
| 99. D8 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548656 | 2 |
| C4×D2008 | 2 |
| #30631514 | 2 |
| #30631488 | 2 |
| #30631487 | 2 |
| #30631463 | 2 |
| C4×D8×C251 | 2 |
| #2177 | 251 |