Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 3. #30631889 | C2 | direct (N × H) |
| 4. C2×C4⋊(C251⋊C8) | C2 | semidirect |
| 5. C2×#22548639 | C2 | semidirect |
| 6. C2×C4⋊Q8×C251 | C2 | semidirect |
| 16. C4⋊(C251⋊C8) | C22 | semidirect |
| 17. #22548639 | C22 | semidirect |
| 20. C4⋊Q8×C251 | C22 | semidirect |
| 68. C2×C4×C251 | SD16 | semidirect |
| 86. C4×C251 | C2×SD16 | semidirect |
| 90. C2×C251 | #461 | semidirect |
| 95. C251 | C2×#461 | semidirect |
| 98. C2×C4⋊Q8 | D251 | semidirect |
| 110. C4⋊Q8 | C2×D251 | semidirect |
| 163. C2×C4 | #16860797 | semidirect |
| 183. C4 | C2×#16860797 | semidirect |
| 187. C2 | #30631889 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860797 | 2 |
| C2×C4×D1004 | 2 |
| #30631889 | 2 |
| C2×C4⋊(C251⋊C8) | 2 |
| C2×#22548639 | 2 |
| C2×C4⋊Q8×C251 | 2 |
| C2×#461 | 251 |