Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
564 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 189 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. #30631593 | C2 | semidirect |
| 3. #30631585 | C2 | semidirect |
| 4. #30631571 | C2 | semidirect |
| 45. C22×C4×C251 | Q8 | semidirect |
| 102. C251 | #2855 | semidirect |
| 142. C22×C4 | Dic502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548694 | 2 |
| #30631593 | 2 |
| #30631585 | 2 |
| #30631571 | 2 |
| #30631560 | 2 |
| #30631550 | 2 |
| #30631547 | 2 |
| C22×C42×C251 | 2 |
| #2855 | 251 |