Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C2×#22548642 | C2 | semidirect |
| 3. C2×#22548641 | C2 | semidirect |
| 4. #30631686 | C2 | semidirect |
| 5. C2×#22548631 | C2 | semidirect |
| 6. #30631588 | C2 | semidirect |
| 7. #417×C251 | C2 | semidirect |
| 11. #22548761 | C4 | semidirect |
| 19. C2×#16860794 | C22 | semidirect |
| 21. C2×C4×Dic251 | C22 | semidirect |
| 28. C2×M16×C251 | C22 | semidirect |
| 29. C2×C4⋊C4×C251 | C22 | semidirect |
| 93. Dic502 | C22⋊C4 | semidirect |
| 100. D1004 | C22⋊C4 | semidirect |
| 115. Q8×C251 | C22⋊C4 | semidirect |
| 119. D4×C251 | C22⋊C4 | semidirect |
| 165. C251 | #1792 | semidirect |
| 171. #417 | D251 | semidirect |
| 187. C2×M16 | C2×D251 | semidirect |
| 188. C2×C4⋊C4 | C2×D251 | semidirect |
| 263. Q8 | (C2×D251)⋊C4 | semidirect |
| 277. D4 | (C2×D251)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548761 | 2 |
| C2×#22548642 | 2 |
| C2×#22548641 | 2 |
| #30631686 | 2 |
| C2×#22548631 | 2 |
| #30631588 | 2 |
| #417×C251 | 2 |
| #1792 | 251 |