Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
380 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 3. #30631547 | C2 | semidirect |
| 4. #30631453 | C2 | semidirect |
| 5. #380×C251 | C2 | semidirect |
| 7. C22×C4×D251 | C4 | semidirect |
| 13. C2×Dic251⋊C4 | C4 | semidirect |
| 16. C2×(C2×D251)⋊C4 | C4 | semidirect |
| 17. C2×C4×Dic251 | C4 | semidirect |
| 65. C22×D251 | C4⋊C4 | semidirect |
| 79. C2×Dic251 | C4⋊C4 | semidirect |
| 130. C4×C251 | #99 | semidirect |
| 145. C251 | #1799 | semidirect |
| 150. #380 | D251 | semidirect |
| 280. C4 | #22548629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D251 | 2 |
| C2×#22548629 | 2 |
| #30631547 | 2 |
| #30631453 | 2 |
| #380×C251 | 2 |
| #1799 | 251 |