Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×Q16×D251 | C2 | semidirect |
| 4. #30632066 | C2 | semidirect |
| 5. #30631927 | C2 | semidirect |
| 6. #30631898 | C2 | semidirect |
| 7. #30631844 | C2 | semidirect |
| 8. #30631841 | C2 | semidirect |
| 9. C4×#16860800 | C2 | semidirect |
| 11. #462×C251 | C2 | semidirect |
| 57. #16860800 | D4 | semidirect |
| 89. D1004 | Q16 | semidirect |
| 114. C2×D251 | C2×Q16 | semidirect |
| 119. C4×C251 | C2×Q16 | semidirect |
| 130. C251 | D4×Q16 | semidirect |
| 138. #462 | D251 | semidirect |
| 254. C4 | Q16×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D251 | 2 |
| Q8×D1004 | 2 |
| #30632352 | 2 |
| #30632066 | 2 |
| #30631927 | 2 |
| #30631898 | 2 |
| #30631844 | 2 |
| #30631841 | 2 |
| C4×#16860800 | 2 |
| #30631752 | 2 |
| #462×C251 | 2 |
| D4×Q16 | 251 |