Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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×#22548656 | C2 | semidirect |
| 2. #30632064 | C2 | semidirect |
| 3. C4×C251⋊C16 | C2 | semidirect |
| 4. #493×C251 | C2 | semidirect |
| 18. C251⋊C16 | D4 | semidirect |
| 43. C4×C251 | D16 | semidirect |
| 50. C251 | #2246 | semidirect |
| 54. #493 | D251 | semidirect |
| 94. C4 | #22548656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548656 | 2 |
| #30632064 | 2 |
| C4×C251⋊C16 | 2 |
| #493×C251 | 2 |
| #2246 | 251 |