Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
480 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 237 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. #30631794 | C2 | direct (N × H) |
| 18. C2×Q16×C251 | C4 | semidirect |
| 37. Q16×C251 | C2×C4 | semidirect |
| 65. C2×C251 | #441 | semidirect |
| 68. C251 | C2×#441 | semidirect |
| 77. C2×Q16 | Dic251 | semidirect |
| 98. Q16 | C2×Dic251 | semidirect |
| 134. C2 | #30631794 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic251 | 2 |
| #30631794 | 2 |
| C2×#22548647 | 2 |
| C2×#22548639 | 2 |
| C2×#22548625 | 2 |
| C22×Q16×C251 | 2 |
| C2×#441 | 251 |