Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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. C4×#16860794 | C2 | semidirect |
| 3. #30631414 | C2 | semidirect |
| 4. #432×C251 | C2 | semidirect |
| 15. C4×C251⋊C8 | C22 | semidirect |
| 17. C4⋊C8×C251 | C22 | semidirect |
| 48. D1004 | M16 | semidirect |
| 85. C251 | #1490 | semidirect |
| 88. #432 | D251 | semidirect |
| 101. C4⋊C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1004 | 2 |
| C4×#16860794 | 2 |
| #30631414 | 2 |
| #432×C251 | 2 |
| #1490 | 251 |