Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 145 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. #30632237 | C2 | semidirect |
| 2. #30632090 | C2 | semidirect |
| 3. #30632063 | C2 | semidirect |
| 4. #30632035 | C2 | semidirect |
| 5. #30632033 | C2 | semidirect |
| 6. #30631921 | C2 | semidirect |
| 7. C4×#16860795 | C2 | semidirect |
| 8. C2×C4×C251⋊C8 | C2 | semidirect |
| 9. #532×C251 | C2 | semidirect |
| 77. C251⋊C8 | #41 | semidirect |
| 89. C2×C4×C251 | D8 | semidirect |
| 120. C251 | #3169 | semidirect |
| 123. #532 | D251 | semidirect |
| 208. C2×C4 | #16860795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632237 | 2 |
| #30632090 | 2 |
| #30632063 | 2 |
| #30632035 | 2 |
| #30632033 | 2 |
| #30631921 | 2 |
| C4×#16860795 | 2 |
| C2×C4×C251⋊C8 | 2 |
| #532×C251 | 2 |
| #3169 | 251 |