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×#22548723 | C2 | semidirect |
| 3. #30632261 | C2 | semidirect |
| 4. #30631942 | C2 | semidirect |
| 5. #30631930 | C2 | semidirect |
| 6. #30631925 | C2 | semidirect |
| 7. #30631913 | C2 | semidirect |
| 8. #30631729 | C2 | semidirect |
| 9. #30631683 | C2 | semidirect |
| 10. C2×#22548639 | C2 | semidirect |
| 11. C2×#137×C251 | C2 | semidirect |
| 83. M16×C251 | D4 | semidirect |
| 143. C251 | #3063 | semidirect |
| 145. C2×#137 | D251 | semidirect |
| 210. M16 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548723 | 2 |
| #30632265 | 2 |
| #30632261 | 2 |
| #30631942 | 2 |
| #30631930 | 2 |
| #30631925 | 2 |
| #30631913 | 2 |
| #30631729 | 2 |
| #30631683 | 2 |
| C2×#22548639 | 2 |
| C2×#137×C251 | 2 |
| #3063 | 251 |