Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22548747 | C2 | semidirect |
| 3. C4×Q8×D251 | C2 | semidirect |
| 4. #30631912 | C2 | semidirect |
| 5. #30631911 | C2 | semidirect |
| 6. #30631894 | C2 | semidirect |
| 7. #30631888 | C2 | semidirect |
| 8. #30631887 | C2 | semidirect |
| 9. #30631709 | C2 | semidirect |
| 10. #30631687 | C2 | semidirect |
| 11. #462×C251 | C2 | semidirect |
| 49. Q8×D251 | D4 | semidirect |
| 133. C4×C251 | #137 | semidirect |
| 146. C251 | #3037 | semidirect |
| 154. #462 | D251 | semidirect |
| 285. C4 | #22548747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548747 | 2 |
| #30632238 | 2 |
| C4×Q8×D251 | 2 |
| #30631912 | 2 |
| #30631911 | 2 |
| #30631894 | 2 |
| #30631888 | 2 |
| #30631887 | 2 |
| #30631709 | 2 |
| #30631687 | 2 |
| #462×C251 | 2 |
| #3037 | 251 |