Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
164 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#22548654 | C2 | semidirect |
| 3. Dic251⋊C16 | C2 | semidirect |
| 4. C22⋊(C251⋊C16) | C2 | semidirect |
| 5. (C2×D251)⋊C16 | C2 | semidirect |
| 6. #30631462 | C2 | semidirect |
| 7. C22×C16×C251 | C2 | semidirect |
| 39. C16×C251 | D4 | semidirect |
| 59. C22×C251 | M32 | semidirect |
| 75. C251 | #2168 | semidirect |
| 78. C22×C16 | D251 | semidirect |
| 115. C16 | C22⋊D251 | semidirect |
| 138. C22 | #22548654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548654 | 2 |
| C8×C22⋊D251 | 2 |
| Dic251⋊C16 | 2 |
| C22⋊(C251⋊C16) | 2 |
| (C2×D251)⋊C16 | 2 |
| #30631462 | 2 |
| C22×C16×C251 | 2 |
| #2168 | 251 |