Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. D4×Dic502 | C2 | semidirect |
| 2. #30632034 | C2 | semidirect |
| 3. #30631888 | C2 | semidirect |
| 5. #30631434 | C2 | semidirect |
| 6. #30631419 | C2 | semidirect |
| 7. D4⋊C8×C251 | C2 | semidirect |
| 56. Dic502 | D8 | semidirect |
| 69. D4×C251 | SD16 | semidirect |
| 99. C251 | #1627 | semidirect |
| 107. D4⋊C8 | D251 | semidirect |
| 164. D4 | #16860799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic502 | 2 |
| #30632034 | 2 |
| #30631888 | 2 |
| #30631882 | 2 |
| #30631434 | 2 |
| #30631419 | 2 |
| D4⋊C8×C251 | 2 |
| #1627 | 251 |