Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
284 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 77 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. #30631482 | C2 | direct (N × H) |
| 7. C22×Q8×C251 | C4 | semidirect |
| 10. #124×C251 | C4 | semidirect |
| 13. C2×C42×C251 | C4 | semidirect |
| 21. C2×Q8×C251 | C2×C4 | semidirect |
| 33. C42×C251 | C2×C4 | semidirect |
| 75. C2×C251 | #354 | semidirect |
| 77. C251 | C2×#354 | semidirect |
| 82. C22×Q8 | Dic251 | semidirect |
| 85. #124 | Dic251 | semidirect |
| 89. C2×C42 | Dic251 | semidirect |
| 96. C2×Q8 | C2×Dic251 | semidirect |
| 111. C42 | C2×Dic251 | semidirect |
| 153. C2 | #30631482 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548630 | 2 |
| #30631482 | 2 |
| C2×#124×C251 | 2 |
| C2×#354 | 251 |