Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #30632000 | C2 | semidirect |
| 3. #30631982 | C2 | semidirect |
| 4. #30631887 | C2 | semidirect |
| 5. #30631826 | C2 | semidirect |
| 6. #30631785 | C2 | semidirect |
| 7. #30631744 | C2 | semidirect |
| 8. C2×C4×Q8×C251 | C2 | semidirect |
| 76. Q8×C251 | #41 | semidirect |
| 111. C251 | #3112 | semidirect |
| 114. C2×C4×Q8 | D251 | semidirect |
| 181. Q8 | #16860810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632237 | 2 |
| #30632000 | 2 |
| #30631982 | 2 |
| #30631887 | 2 |
| #30631826 | 2 |
| #30631785 | 2 |
| #30631744 | 2 |
| C2×C4×Q8×C251 | 2 |
| #3112 | 251 |