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. Q8×D1004 | C2 | semidirect |
| 2. #30632034 | C2 | semidirect |
| 3. #30631887 | C2 | semidirect |
| 5. #30631432 | C2 | semidirect |
| 6. #30631416 | C2 | semidirect |
| 7. Q8⋊C8×C251 | C2 | semidirect |
| 62. D1004 | SD16 | semidirect |
| 70. Q8×C251 | D8 | semidirect |
| 99. C251 | #1627 | semidirect |
| 106. Q8⋊C8 | D251 | semidirect |
| 157. Q8 | D2008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D1004 | 2 |
| #30632034 | 2 |
| #30631887 | 2 |
| #30631883 | 2 |
| #30631432 | 2 |
| #30631416 | 2 |
| Q8⋊C8×C251 | 2 |
| #1627 | 251 |