Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. C2×#22548634 | C2 | semidirect |
| 4. #30631446 | C2 | semidirect |
| 5. #519×C251 | C2 | semidirect |
| 9. #22548704 | C4 | semidirect |
| 79. C251 | #1888 | semidirect |
| 82. #519 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548704 | 2 |
| #30631691 | 2 |
| C2×#22548634 | 2 |
| #30631446 | 2 |
| #519×C251 | 2 |
| #1888 | 251 |