Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
752 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#22548704 | C2 | semidirect |
| 3. #30631588 | C2 | semidirect |
| 4. C42×Dic251 | C2 | semidirect |
| 5. C2×C4⋊Q8×C251 | C2 | semidirect |
| 25. C4×Dic251 | D4 | semidirect |
| 55. C4×C251 | #124 | semidirect |
| 62. C251 | #2858 | semidirect |
| 64. C2×C4⋊Q8 | D251 | semidirect |
| 119. C4 | #22548704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548712 | 2 |
| C2×#22548704 | 2 |
| #30631588 | 2 |
| C42×Dic251 | 2 |
| C2×C4⋊Q8×C251 | 2 |
| #2858 | 251 |