Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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×#22548659 | C2 | semidirect |
| 2. C4×Dic1004 | C2 | semidirect |
| 3. C4⋊(C251⋊C16) | C2 | semidirect |
| 4. #30631488 | C2 | semidirect |
| 18. Dic1004 | D4 | semidirect |
| 52. C4×C251 | SD32 | semidirect |
| 61. C251 | #2207 | semidirect |
| 116. C4 | #22548659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548659 | 2 |
| C4×Dic1004 | 2 |
| C4⋊(C251⋊C16) | 2 |
| #30631488 | 2 |
| #493×C251 | 2 |
| #2207 | 251 |