Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
186 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 51 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. #30632062 | C2 | semidirect |
| 3. D8×Dic251 | C2 | semidirect |
| 4. Dic251⋊C16 | C2 | semidirect |
| 5. #30631489 | C2 | semidirect |
| 6. #30631488 | C2 | semidirect |
| 7. C2×D16×C251 | C2 | semidirect |
| 38. D8×C251 | D4 | semidirect |
| 74. Dic251 | D16 | semidirect |
| 81. C251 | #2206 | semidirect |
| 84. C2×D16 | D251 | semidirect |
| 115. D8 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548656 | 2 |
| #30632062 | 2 |
| D8×Dic251 | 2 |
| Dic251⋊C16 | 2 |
| #30631489 | 2 |
| #30631488 | 2 |
| C2×D16×C251 | 2 |
| #2206 | 251 |