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 |
| 3. #30631925 | C2 | semidirect |
| 4. #30631894 | C2 | semidirect |
| 5. #30631841 | C2 | semidirect |
| 6. C4×Dic1004 | C2 | semidirect |
| 8. #494×C251 | C2 | semidirect |
| 36. Dic1004 | D4 | semidirect |
| 59. D1004 | Q16 | semidirect |
| 78. C2×D251 | C2×Q16 | semidirect |
| 81. C4×C251 | C2×Q16 | semidirect |
| 91. C251 | D4×Q16 | semidirect |
| 95. #494 | D251 | semidirect |
| 176. 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 |
| #30632352 | 2 |
| #30631925 | 2 |
| #30631894 | 2 |
| #30631841 | 2 |
| C4×Dic1004 | 2 |
| C8×D1004 | 2 |
| #494×C251 | 2 |
| D4×Q16 | 251 |