Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. #30632453 | C2 | semidirect |
| 3. #30631692 | C2 | semidirect |
| 4. #30631660 | C2 | semidirect |
| 5. #30631444 | C2 | semidirect |
| 6. #30631443 | C2 | semidirect |
| 7. #418×C251 | C2 | semidirect |
| 13. #22548711 | C4 | semidirect |
| 14. #22548702 | C4 | semidirect |
| 37. C2×C251⋊C8 | D4 | semidirect |
| 56. C2×C8×C251 | D4 | semidirect |
| 115. C251 | #1910 | semidirect |
| 120. #418 | D251 | semidirect |
| 165. C2×C8 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632453 | 2 |
| #30632254 | 2 |
| #30631692 | 2 |
| #30631660 | 2 |
| #30631444 | 2 |
| #30631443 | 2 |
| #418×C251 | 2 |
| #1910 | 251 |