Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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. #30631487 | C2 | semidirect |
| 5. C4×D8×C251 | C2 | semidirect |
| 26. D8×C251 | D4 | semidirect |
| 57. C4×C251 | D16 | semidirect |
| 65. C251 | #2206 | semidirect |
| 69. C4×D8 | D251 | semidirect |
| 91. D8 | D1004 | semidirect |
| 123. 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 |
| #30631487 | 2 |
| C4×D8×C251 | 2 |
| #2206 | 251 |