Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
402 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 161 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. #30631766 | C2 | semidirect |
| 3. #30631757 | C2 | semidirect |
| 4. C8×D1004 | C2 | semidirect |
| 5. #30631744 | C2 | semidirect |
| 6. #30631652 | C2 | semidirect |
| 7. #431×C251 | C2 | semidirect |
| 92. C251 | #2981 | semidirect |
| 99. #431 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632237 | 2 |
| #30631766 | 2 |
| #30631757 | 2 |
| C8×D1004 | 2 |
| #30631744 | 2 |
| #30631652 | 2 |
| #431×C251 | 2 |
| #2981 | 251 |