Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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×#22548746 | C2 | semidirect |
| 3. #30631909 | C2 | semidirect |
| 4. #30631897 | C2 | semidirect |
| 5. #30631887 | C2 | semidirect |
| 6. #30631711 | C2 | semidirect |
| 7. #30631686 | C2 | semidirect |
| 8. C2×C4×Q8×C251 | C2 | semidirect |
| 52. C2×Q8×C251 | D4 | semidirect |
| 111. C4×C251 | #137 | semidirect |
| 120. C251 | #3037 | semidirect |
| 124. C2×C4×Q8 | D251 | semidirect |
| 160. C2×Q8 | D1004 | semidirect |
| 233. C4 | #22548746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548746 | 2 |
| #30632237 | 2 |
| #30631909 | 2 |
| #30631897 | 2 |
| #30631887 | 2 |
| #30631711 | 2 |
| #30631686 | 2 |
| C2×C4×Q8×C251 | 2 |
| #3037 | 251 |