Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
578 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 97 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. #30632162 | C2 | semidirect |
| 2. C2×#22548630 | C2 | semidirect |
| 3. #30631543 | C2 | semidirect |
| 4. #30631453 | C2 | semidirect |
| 17. #120×C251 | C4 | semidirect |
| 22. C22×Dic251 | D4 | semidirect |
| 36. C24×C251 | C2×C4 | semidirect |
| 49. C22⋊C4×C251 | C2×C4 | semidirect |
| 71. C23×C251 | C22⋊C4 | semidirect |
| 84. C2×C4×C251 | C22⋊C4 | semidirect |
| 119. C251 | #1889 | semidirect |
| 130. #120 | Dic251 | semidirect |
| 145. C24 | C2×Dic251 | semidirect |
| 168. C22⋊C4 | C2×Dic251 | semidirect |
| 186. C23 | C22⋊Dic251 | semidirect |
| 204. C2×C4 | C22⋊Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632162 | 2 |
| C2×#22548630 | 2 |
| #30631543 | 2 |
| #30631453 | 2 |
| C2×#120×C251 | 2 |
| #1889 | 251 |