Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#22548745 | C2 | semidirect |
| 2. C2×#22548694 | C2 | semidirect |
| 3. #30631849 | C2 | semidirect |
| 4. #30631843 | C2 | semidirect |
| 5. #30631838 | C2 | semidirect |
| 6. #30631688 | C2 | semidirect |
| 7. #30631651 | C2 | semidirect |
| 9. C22×Dic502 | C22 | semidirect |
| 11. C2×#16860800 | C22 | semidirect |
| 12. C2×#16860798 | C22 | semidirect |
| 13. C2×#16860794 | C22 | semidirect |
| 17. #22548694 | C22 | semidirect |
| 18. C2×C4⋊Dic251 | C22 | semidirect |
| 21. #22548639 | C22 | semidirect |
| 22. #22548636 | C22 | semidirect |
| 24. C22⋊(C251⋊C8) | C22 | semidirect |
| 130. C22×C251 | #137 | semidirect |
| 146. C251 | #3007 | semidirect |
| 277. C22 | #22548745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548745 | 2 |
| C2×#22548694 | 2 |
| #30631849 | 2 |
| #30631843 | 2 |
| #30631838 | 2 |
| #30631688 | 2 |
| #30631651 | 2 |
| C22×#41×C251 | 2 |
| #3007 | 251 |