Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
284 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 67 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. #97×D251 | C2 | semidirect |
| 3. #30631427 | C2 | semidirect |
| 4. #30631426 | C2 | semidirect |
| 5. #329×C251 | C2 | semidirect |
| 15. #22548626 | C22 | semidirect |
| 18. #97×C251 | C22 | semidirect |
| 81. D251 | #329 | direct (N × H) |
| 82. C251 | C2×#329 | semidirect |
| 88. #329 | D251 | direct (N × H) |
| 101. #97 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #124×D251 | 2 |
| #97×D251 | 2 |
| #30631427 | 2 |
| #30631426 | 2 |
| #329×C251 | 2 |
| C2×#329 | 251 |