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×#22548746 | C2 | semidirect |
| 2. C2×#22548722 | C2 | semidirect |
| 4. #30631943 | C2 | semidirect |
| 5. #30631935 | C2 | semidirect |
| 6. #30631926 | C2 | semidirect |
| 7. #30631918 | C2 | semidirect |
| 8. #30631730 | C2 | semidirect |
| 9. #30631681 | C2 | semidirect |
| 10. C2×#22548639 | C2 | semidirect |
| 11. #536×C251 | C2 | semidirect |
| 54. #16860794 | D4 | semidirect |
| 143. C251 | #3063 | semidirect |
| 148. #536 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548746 | 2 |
| C2×#22548722 | 2 |
| #30632265 | 2 |
| #30631943 | 2 |
| #30631935 | 2 |
| #30631926 | 2 |
| #30631918 | 2 |
| #30631730 | 2 |
| #30631681 | 2 |
| C2×#22548639 | 2 |
| #536×C251 | 2 |
| #3063 | 251 |