Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
608 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×D1004 | C2 | semidirect |
| 3. #30631800 | C2 | direct (N × H) |
| 4. C2×#22548647 | C2 | semidirect |
| 5. C2×#22548637 | C2 | semidirect |
| 6. C2×#97×C251 | C2 | semidirect |
| 9. C2×D2008 | C4 | semidirect |
| 12. C4×D1004 | C22 | semidirect |
| 15. #22548647 | C22 | semidirect |
| 16. #22548637 | C22 | semidirect |
| 20. #97×C251 | C22 | semidirect |
| 24. C2×D1004 | C2×C4 | semidirect |
| 29. D2008 | C2×C4 | semidirect |
| 36. C2×C8×C251 | C2×C4 | semidirect |
| 47. D1004 | C22×C4 | semidirect |
| 59. C8×C251 | C22×C4 | semidirect |
| 72. C2×C251 | #442 | semidirect |
| 76. C251 | C2×#442 | semidirect |
| 83. C2×#97 | D251 | semidirect |
| 97. #97 | C2×D251 | semidirect |
| 110. C2×C8 | C4×D251 | semidirect |
| 136. C8 | C2×C4×D251 | semidirect |
| 150. C2 | #30631800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2008 | 2 |
| C2×C4×D1004 | 2 |
| #30631800 | 2 |
| C2×#22548647 | 2 |
| C2×#22548637 | 2 |
| C2×#97×C251 | 2 |
| C2×#442 | 251 |