Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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. #30631766 | C2 | semidirect |
| 3. #30631439 | C2 | semidirect |
| 4. D4⋊(C251⋊C8) | C2 | semidirect |
| 5. #30631414 | C2 | semidirect |
| 6. C8×C251⋊C8 | C2 | semidirect |
| 7. #436×C251 | C2 | semidirect |
| 51. C251⋊C8 | M16 | semidirect |
| 63. C8×C251 | D8 | semidirect |
| 83. C251 | #1589 | semidirect |
| 87. #436 | D251 | semidirect |
| 147. C8 | #16860795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16860795 | 2 |
| #30631766 | 2 |
| #30631439 | 2 |
| D4⋊(C251⋊C8) | 2 |
| #30631414 | 2 |
| C8×C251⋊C8 | 2 |
| #436×C251 | 2 |
| #1589 | 251 |