Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 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×#22548734 | C2 | semidirect |
| 2. #30632235 | C2 | semidirect |
| 3. C4×#16860809 | C2 | semidirect |
| 4. #30631908 | C2 | semidirect |
| 5. #30631900 | C2 | semidirect |
| 6. #30631898 | C2 | semidirect |
| 7. #30631892 | C2 | semidirect |
| 8. #30631884 | C2 | semidirect |
| 9. C4⋊C8×D251 | C2 | semidirect |
| 10. #30631680 | C2 | semidirect |
| 11. #459×C251 | C2 | semidirect |
| 47. #16860809 | D4 | semidirect |
| 135. C4×C251 | #135 | semidirect |
| 150. C251 | #3035 | semidirect |
| 160. #459 | D251 | semidirect |
| 292. C4 | #22548734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548734 | 2 |
| #30632235 | 2 |
| C4×#16860809 | 2 |
| #30631908 | 2 |
| #30631900 | 2 |
| #30631898 | 2 |
| #30631892 | 2 |
| #30631884 | 2 |
| C4⋊C8×D251 | 2 |
| #30631680 | 2 |
| #459×C251 | 2 |
| #3035 | 251 |