Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
266 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 93 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. #30631711 | C2 | semidirect |
| 2. C4×#16860794 | C2 | semidirect |
| 3. Q8⋊(C251⋊C8) | C2 | semidirect |
| 4. D4⋊(C251⋊C8) | C2 | semidirect |
| 57. Q8×C251 | M16 | semidirect |
| 60. D4×C251 | M16 | semidirect |
| 102. C251 | #1489 | semidirect |
| 158. Q8 | #16860794 | semidirect |
| 161. D4 | #16860794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631711 | 2 |
| C4×#16860794 | 2 |
| Q8⋊(C251⋊C8) | 2 |
| D4⋊(C251⋊C8) | 2 |
| C4×#41×C251 | 2 |
| #1489 | 251 |