Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×#16860793 | C2 | semidirect |
| 3. C2×C4⋊C4×D251 | C2 | semidirect |
| 4. #30631685 | C2 | direct (N × H) |
| 5. C2×#22548640 | C2 | semidirect |
| 6. C2×#22548638 | C2 | semidirect |
| 7. C2×#22548636 | C2 | semidirect |
| 8. C2×#102×C251 | C2 | semidirect |
| 11. C2×#16860809 | C4 | semidirect |
| 19. C2×#16860793 | C22 | semidirect |
| 24. C4⋊C4×D251 | C22 | semidirect |
| 25. #22548640 | C22 | semidirect |
| 26. #22548638 | C22 | semidirect |
| 27. #22548636 | C22 | semidirect |
| 31. #102×C251 | C22 | semidirect |
| 35. #16860809 | C2×C4 | semidirect |
| 38. C2×Dic502 | C2×C4 | semidirect |
| 62. C2×D4×C251 | C2×C4 | semidirect |
| 76. Dic502 | C22×C4 | semidirect |
| 97. D4×C251 | C22×C4 | semidirect |
| 125. C2×C251 | #417 | semidirect |
| 130. C251 | C2×#417 | semidirect |
| 139. C2×#102 | D251 | semidirect |
| 162. #102 | C2×D251 | semidirect |
| 176. C2×D4 | C4×D251 | semidirect |
| 216. D4 | C2×C4×D251 | semidirect |
| 257. C2 | #30631685 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860809 | 2 |
| C22×#16860793 | 2 |
| C2×C4⋊C4×D251 | 2 |
| #30631685 | 2 |
| C2×#22548640 | 2 |
| C2×#22548638 | 2 |
| C2×#22548636 | 2 |
| C2×#102×C251 | 2 |
| C2×#417 | 251 |