Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 444 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. #30631626 | C2 | semidirect |
| 3. #30631625 | C2 | semidirect |
| 5. #30631607 | C2 | semidirect |
| 6. #30631606 | C2 | semidirect |
| 92. C251 | #2817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548694 | 2 |
| #30631626 | 2 |
| #30631625 | 2 |
| #30631615 | 2 |
| #30631607 | 2 |
| #30631606 | 2 |
| #30631550 | 2 |
| C2×C22⋊Q8×C251 | 2 |
| #2817 | 251 |