Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
376 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 3. #30631996 | C2 | semidirect |
| 4. #30631992 | C2 | semidirect |
| 5. #30631980 | C2 | semidirect |
| 6. #30631970 | C2 | semidirect |
| 72. C2×Q8×C251 | Q8 | semidirect |
| 129. C251 | #3078 | semidirect |
| 177. C2×Q8 | Dic502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632240 | 2 |
| C2×Q8×Dic251 | 2 |
| #30631996 | 2 |
| #30631992 | 2 |
| #30631980 | 2 |
| #30631970 | 2 |
| #30631730 | 2 |
| #30631729 | 2 |
| #30631710 | 2 |
| #30631696 | 2 |
| #419×C251 | 2 |
| #3078 | 251 |