Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
766 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 766 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 |
|---|---|---|
| 1. #30632194 | C2 | semidirect |
| 2. #30631877 | C2 | semidirect |
| 3. #30631874 | C2 | semidirect |
| 4. #30631661 | C2 | semidirect |
| 5. #585×C251 | C2 | semidirect |
| 6. C22×C4×D251 | C22 | semidirect |
| 7. #22548696 | C22 | semidirect |
| 10. #22548683 | C22 | semidirect |
| 12. #22548674 | C22 | semidirect |
| 13. #22548630 | C22 | semidirect |
| 36. C2×Q8×C251 | D4 | semidirect |
| 39. C2×D4×C251 | D4 | semidirect |
| 42. C22×C4×C251 | D4 | semidirect |
| 82. C251 | #3025 | semidirect |
| 84. #585 | D251 | semidirect |
| 109. C2×Q8 | C22⋊D251 | semidirect |
| 113. C2×D4 | C22⋊D251 | semidirect |
| 119. C22×C4 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632194 | 2 |
| #30631877 | 2 |
| #30631874 | 2 |
| #30631661 | 2 |
| #585×C251 | 2 |
| #3025 | 251 |