Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
438 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 113 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×#22548636 | C2 | semidirect |
| 3. C2×#22548635 | C2 | semidirect |
| 4. #30631589 | C2 | semidirect |
| 5. #30631449 | C2 | semidirect |
| 6. #30631442 | C2 | semidirect |
| 7. C2×C4×D4×C251 | C2 | semidirect |
| 11. C2×#16860795 | C4 | semidirect |
| 32. C2×D1004 | C2×C4 | semidirect |
| 40. C2×C251⋊C8 | C2×C4 | semidirect |
| 91. D4×C251 | C22⋊C4 | semidirect |
| 101. C2×C4×C251 | D8 | semidirect |
| 146. C251 | #1879 | semidirect |
| 149. C2×C4×D4 | D251 | semidirect |
| 233. D4 | (C2×D251)⋊C4 | semidirect |
| 246. C2×C4 | #16860795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860795 | 2 |
| C2×#22548636 | 2 |
| C2×#22548635 | 2 |
| #30631589 | 2 |
| #30631449 | 2 |
| #30631442 | 2 |
| C2×C4×D4×C251 | 2 |
| #1879 | 251 |