Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. #30632025 | C2 | direct (N × H) |
| 3. C2×#22548648 | C2 | semidirect |
| 4. C2×#22548646 | C2 | semidirect |
| 5. C2×#22548639 | C2 | semidirect |
| 6. C2×#22548639 | C2 | semidirect |
| 17. #22548648 | C22 | semidirect |
| 18. #22548646 | C22 | semidirect |
| 19. #22548639 | C22 | semidirect |
| 20. #22548639 | C22 | semidirect |
| 102. C2×C251 | #485 | semidirect |
| 106. C251 | C2×#485 | semidirect |
| 209. C2 | #30632025 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548674 | 2 |
| #30632025 | 2 |
| C2×#22548648 | 2 |
| C2×#22548646 | 2 |
| C2×#22548639 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×C22⋊Q8×C251 | 2 |
| C2×#485 | 251 |