Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
500 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16860800 | C2 | semidirect |
| 4. #30631909 | C2 | direct (N × H) |
| 5. C2×C4⋊(C251⋊C8) | C2 | semidirect |
| 6. C2×#22548638 | C2 | semidirect |
| 8. C2×C4×Q8×C251 | C2 | semidirect |
| 12. C2×#16860800 | C22 | semidirect |
| 21. C4⋊(C251⋊C8) | C22 | semidirect |
| 22. #22548638 | C22 | semidirect |
| 26. C4×Q8×C251 | C22 | semidirect |
| 110. C2×C251 | #464 | semidirect |
| 115. C251 | C2×#464 | semidirect |
| 120. C2×C4×Q8 | D251 | semidirect |
| 137. C4×Q8 | C2×D251 | semidirect |
| 227. C2 | #30631909 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860800 | 2 |
| C22×#16860797 | 2 |
| C2×#22548703 | 2 |
| #30631909 | 2 |
| C2×C4⋊(C251⋊C8) | 2 |
| C2×#22548638 | 2 |
| C2×#22548635 | 2 |
| C2×C4×Q8×C251 | 2 |
| C2×#464 | 251 |