Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22548748 | C2 | semidirect |
| 2. C2×#22548723 | C2 | semidirect |
| 4. #30632263 | C2 | semidirect |
| 5. #30631946 | C2 | semidirect |
| 6. #30631934 | C2 | semidirect |
| 7. #30631929 | C2 | semidirect |
| 8. #30631917 | C2 | semidirect |
| 9. #30631681 | C2 | semidirect |
| 10. C2×#22548638 | C2 | semidirect |
| 11. #428×C251 | C2 | semidirect |
| 77. M16×C251 | D4 | semidirect |
| 143. C251 | #3063 | semidirect |
| 153. #428 | D251 | semidirect |
| 210. M16 | D1004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548748 | 2 |
| C2×#22548723 | 2 |
| #30632268 | 2 |
| #30632263 | 2 |
| #30631946 | 2 |
| #30631934 | 2 |
| #30631929 | 2 |
| #30631917 | 2 |
| #30631681 | 2 |
| C2×#22548638 | 2 |
| #428×C251 | 2 |
| #3063 | 251 |