Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
704 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 237 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. #30631585 | C2 | semidirect |
| 4. #30631558 | C2 | semidirect |
| 5. #30631553 | C2 | semidirect |
| 6. #30631546 | C2 | semidirect |
| 7. #95×D251 | C2 | semidirect |
| 8. C4×C4⋊C4×C251 | C2 | semidirect |
| 13. C4×D1004 | C4 | semidirect |
| 37. C2×C4×D251 | C2×C4 | semidirect |
| 39. C4⋊Dic251 | C2×C4 | semidirect |
| 42. (C2×D251)⋊C4 | C2×C4 | semidirect |
| 50. C42×C251 | C2×C4 | semidirect |
| 56. D1004 | C4⋊C4 | semidirect |
| 101. C251 | #2349 | semidirect |
| 109. C4×C4⋊C4 | D251 | semidirect |
| 152. C42 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1004 | 2 |
| #30631585 | 2 |
| #30631558 | 2 |
| #30631553 | 2 |
| #30631546 | 2 |
| #95×D251 | 2 |
| C4×C4⋊C4×C251 | 2 |
| #2349 | 251 |