Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 93 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×#22548686 | C2 | semidirect |
| 2. C2×#22548636 | C2 | semidirect |
| 3. C2×(C2×D251)⋊C8 | C2 | semidirect |
| 4. #30631450 | C2 | semidirect |
| 5. C22×D8×C251 | C2 | semidirect |
| 32. C4⋊Dic251 | D4 | semidirect |
| 40. C2×D4×C251 | D4 | semidirect |
| 44. C2×C8×C251 | D4 | semidirect |
| 49. C22×D251 | D8 | semidirect |
| 106. C251 | #1999 | semidirect |
| 108. C22×D8 | D251 | semidirect |
| 136. C2×D4 | C22⋊D251 | semidirect |
| 148. C2×C8 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548686 | 2 |
| C2×#22548636 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| #30631450 | 2 |
| C22×D8×C251 | 2 |
| #1999 | 251 |