Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
584 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 181 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×#16860797 | C2 | semidirect |
| 3. #30631887 | C2 | direct (N × H) |
| 4. C2×C4⋊(C251⋊C8) | C2 | semidirect |
| 5. C2×#22548635 | C2 | semidirect |
| 6. C2×C4×Q8×C251 | C2 | semidirect |
| 11. C2×#16860797 | C22 | semidirect |
| 15. C4⋊(C251⋊C8) | C22 | semidirect |
| 16. #22548635 | C22 | semidirect |
| 19. C4×Q8×C251 | C22 | semidirect |
| 38. C2×Q8×C251 | D4 | semidirect |
| 64. Q8×C251 | C2×D4 | semidirect |
| 70. C2×C4×C251 | SD16 | semidirect |
| 89. C4×C251 | C2×SD16 | semidirect |
| 92. C2×C251 | #460 | semidirect |
| 97. C251 | C2×#460 | semidirect |
| 101. C2×C4×Q8 | D251 | semidirect |
| 115. C4×Q8 | C2×D251 | semidirect |
| 125. C2×Q8 | D1004 | semidirect |
| 156. Q8 | C2×D1004 | semidirect |
| 167. C2×C4 | #16860797 | semidirect |
| 187. C4 | C2×#16860797 | semidirect |
| 191. C2 | #30631887 | 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×#22548712 | 2 |
| #30631887 | 2 |
| C2×C4⋊(C251⋊C8) | 2 |
| C2×#22548635 | 2 |
| C2×C4×Q8×C251 | 2 |
| C2×#460 | 251 |