Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#22548735 | C2 | semidirect |
| 2. #30632237 | C2 | semidirect |
| 3. #30632069 | C2 | semidirect |
| 4. #30632066 | C2 | semidirect |
| 5. #30632063 | C2 | semidirect |
| 6. #30632061 | C2 | semidirect |
| 7. #30632059 | C2 | semidirect |
| 8. C2×C4×C251⋊C8 | C2 | semidirect |
| 9. #532×C251 | C2 | semidirect |
| 42. C2×C251⋊C8 | D4 | semidirect |
| 93. C4×C251 | #135 | semidirect |
| 101. C251 | #3147 | semidirect |
| 105. #532 | D251 | semidirect |
| 196. C4 | #22548735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548735 | 2 |
| #30632237 | 2 |
| #30632069 | 2 |
| #30632066 | 2 |
| #30632063 | 2 |
| #30632061 | 2 |
| #30632059 | 2 |
| C2×C4×C251⋊C8 | 2 |
| #532×C251 | 2 |
| #3147 | 251 |