Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
832 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 209 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. C2×C4×C22⋊D251 | C2 | semidirect |
| 3. C2×(C22⋊D251)⋊C4 | C2 | semidirect |
| 4. #30631587 | C2 | semidirect |
| 5. #30631587 | C2 | semidirect |
| 6. #30631567 | C2 | semidirect |
| 7. #30631565 | C2 | semidirect |
| 8. #30631538 | C2 | semidirect |
| 9. #386×C251 | C2 | semidirect |
| 15. #22548711 | C4 | semidirect |
| 37. C2×D1004 | C2×C4 | semidirect |
| 42. C2×C22⋊D251 | C2×C4 | semidirect |
| 43. C2×C22⋊D251 | C2×C4 | semidirect |
| 53. Dic251⋊C4 | D4 | semidirect |
| 61. C4×Dic251 | C2×C4 | semidirect |
| 66. C2×D4×C251 | C2×C4 | semidirect |
| 144. Dic251 | C4×D4 | semidirect |
| 153. C251 | #2366 | semidirect |
| 162. #386 | D251 | semidirect |
| 202. C2×D4 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548711 | 2 |
| C2×C4×C22⋊D251 | 2 |
| C2×(C22⋊D251)⋊C4 | 2 |
| #30631587 | 2 |
| #30631567 | 2 |
| #30631565 | 2 |
| #30631538 | 2 |
| #386×C251 | 2 |
| #2366 | 251 |