Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 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×#22548723 | C2 | semidirect |
| 3. #30631764 | C2 | semidirect |
| 4. #30631752 | C2 | semidirect |
| 5. #30631655 | C2 | semidirect |
| 6. C2×C4×C251⋊C8 | C2 | semidirect |
| 7. #423×C251 | C2 | semidirect |
| 34. C2×C251⋊C8 | D4 | semidirect |
| 75. C4×C251 | #131 | semidirect |
| 83. C251 | #2931 | semidirect |
| 89. #423 | D251 | semidirect |
| 160. C4 | #22548723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548723 | 2 |
| #30632237 | 2 |
| #30631764 | 2 |
| #30631752 | 2 |
| #30631655 | 2 |
| C2×C4×C251⋊C8 | 2 |
| #423×C251 | 2 |
| #2931 | 251 |