Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
728 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 165 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×#22548740 | C2 | semidirect |
| 2. C2×#22548704 | C2 | semidirect |
| 3. #30631860 | C2 | direct (N × H) |
| 4. C2×#22548642 | C2 | semidirect |
| 5. C2×#22548634 | C2 | semidirect |
| 6. C2×2−1+4×C251 | C2 | semidirect |
| 9. #22548740 | C22 | semidirect |
| 14. #22548704 | C22 | semidirect |
| 17. #22548642 | C22 | semidirect |
| 18. #22548634 | C22 | semidirect |
| 21. 2−1+4×C251 | C22 | semidirect |
| 114. C2×C251 | #454 | semidirect |
| 117. C251 | C2×#454 | semidirect |
| 119. C2×2−1+4 | D251 | semidirect |
| 127. 2−1+4 | C2×D251 | semidirect |
| 233. C2 | #30631860 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548740 | 2 |
| C2×#22548704 | 2 |
| #30631860 | 2 |
| C2×#22548642 | 2 |
| C2×#22548634 | 2 |
| C2×2−1+4×C251 | 2 |
| C2×#454 | 251 |