Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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. #30631741 | C2 | semidirect |
| 3. #30631737 | C2 | semidirect |
| 4. #30631412 | C2 | semidirect |
| 5. #30631412 | C2 | semidirect |
| 106. C251 | #1473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548708 | 2 |
| #30631741 | 2 |
| #30631737 | 2 |
| #30631412 | 2 |
| #30631411 | 2 |
| #323×C251 | 2 |
| #1473 | 251 |