Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
452 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 177 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. #30631766 | C2 | semidirect |
| 3. #30631764 | C2 | semidirect |
| 4. #30631740 | C2 | semidirect |
| 5. #30631649 | C2 | semidirect |
| 6. #431×C251 | C2 | semidirect |
| 9. C2×#16860793 | C22 | semidirect |
| 16. C4⋊(C251⋊C8) | C22 | semidirect |
| 18. (C2×D251)⋊C8 | C22 | semidirect |
| 19. C4×C251⋊C8 | C22 | semidirect |
| 21. C4⋊C8×C251 | C22 | semidirect |
| 23. C4×C8×C251 | C22 | semidirect |
| 60. C2×C4×C251 | M16 | semidirect |
| 88. C251 | #2975 | semidirect |
| 94. #431 | D251 | semidirect |
| 107. C4⋊C8 | C2×D251 | semidirect |
| 112. C4×C8 | C2×D251 | semidirect |
| 148. C2×C4 | #16860793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1004 | 2 |
| #30631766 | 2 |
| #30631764 | 2 |
| #30631740 | 2 |
| #30631649 | 2 |
| #431×C251 | 2 |
| #2975 | 251 |