Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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×#22548660 | C2 | semidirect |
| 2. C2×#22548659 | C2 | semidirect |
| 3. C2×#22548656 | C2 | semidirect |
| 4. #30632070 | C2 | semidirect |
| 5. #30632062 | C2 | semidirect |
| 6. #30631462 | C2 | semidirect |
| 7. C2×D16×C251 | C2 | semidirect |
| 35. C251⋊C16 | D4 | semidirect |
| 43. C16×C251 | D4 | semidirect |
| 78. C251 | #2250 | semidirect |
| 83. C2×D16 | D251 | semidirect |
| 122. C16 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548660 | 2 |
| C2×#22548659 | 2 |
| C2×#22548656 | 2 |
| #30632070 | 2 |
| #30632062 | 2 |
| #30631462 | 2 |
| C2×D16×C251 | 2 |
| #2250 | 251 |