Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 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. C2×#22548738 | C2 | semidirect |
| 2. #30632238 | C2 | semidirect |
| 3. #30632072 | C2 | semidirect |
| 4. #30632064 | C2 | semidirect |
| 5. #30632061 | C2 | semidirect |
| 6. C4×C8×D251 | C2 | semidirect |
| 7. #494×C251 | C2 | semidirect |
| 33. C8×D251 | D4 | semidirect |
| 64. C4×C251 | #135 | semidirect |
| 72. C251 | #3147 | semidirect |
| 77. #494 | D251 | semidirect |
| 139. C4 | #22548738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548738 | 2 |
| #30632238 | 2 |
| #30632072 | 2 |
| #30632064 | 2 |
| #30632061 | 2 |
| C4×C8×D251 | 2 |
| #494×C251 | 2 |
| #3147 | 251 |