Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
992 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 309 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. C22×#16860794 | C2 | semidirect |
| 2. C2×#22548632 | C2 | direct (N × H) |
| 5. C2×#16860794 | C22 | semidirect |
| 7. #22548632 | C22 | direct (N × H) |
| 15. #16860794 | C23 | semidirect |
| 57. C22×C251 | #100 | semidirect |
| 66. C2×C251 | C2×#100 | semidirect |
| 68. C251 | C22×#100 | semidirect |
| 126. C22 | #22548632 | direct (N × H) |
| 135. C2 | C2×#22548632 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860794 | 2 |
| C2×#22548632 | 2 |
| C23×D4×C251 | 2 |
| C22×#100 | 251 |