Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#22548714 | C2 | semidirect |
| 3. #30631981 | C2 | semidirect |
| 4. #30631976 | C2 | semidirect |
| 5. #30631971 | C2 | semidirect |
| 6. #30631966 | C2 | semidirect |
| 7. #30631730 | C2 | semidirect |
| 8. #30631710 | C2 | semidirect |
| 11. #428×C251 | C2 | semidirect |
| 44. #16860810 | Q8 | semidirect |
| 87. Dic502 | C2×Q8 | semidirect |
| 89. D1004 | C2×Q8 | semidirect |
| 138. C251 | #3079 | semidirect |
| 147. #428 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548714 | 2 |
| #30632155 | 2 |
| #30631981 | 2 |
| #30631976 | 2 |
| #30631971 | 2 |
| #30631966 | 2 |
| #30631730 | 2 |
| #30631710 | 2 |
| #30631689 | 2 |
| #30631686 | 2 |
| #428×C251 | 2 |
| #3079 | 251 |