Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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. C4×#16860811 | C2 | semidirect |
| 3. #30631800 | C2 | semidirect |
| 4. #30631798 | C2 | semidirect |
| 5. #30631794 | C2 | semidirect |
| 6. #30631790 | C2 | semidirect |
| 7. #30631785 | C2 | semidirect |
| 8. #30631722 | C2 | semidirect |
| 9. #30631682 | C2 | semidirect |
| 10. #97×D251 | C2 | semidirect |
| 11. #441×C251 | C2 | semidirect |
| 13. #22548738 | C4 | semidirect |
| 41. #16860811 | C2×C4 | semidirect |
| 49. #16860797 | C2×C4 | semidirect |
| 50. D2008 | C2×C4 | semidirect |
| 54. C8×D251 | C2×C4 | semidirect |
| 65. Q16×C251 | C2×C4 | semidirect |
| 114. C251 | #2943 | semidirect |
| 121. #441 | D251 | semidirect |
| 165. Q16 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548738 | 2 |
| C4×#16860811 | 2 |
| #30631800 | 2 |
| #30631798 | 2 |
| #30631794 | 2 |
| #30631790 | 2 |
| #30631785 | 2 |
| #30631722 | 2 |
| #30631682 | 2 |
| #97×D251 | 2 |
| #441×C251 | 2 |
| #2943 | 251 |