Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
460 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 213 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. #30631734 | C2 | direct (N × H) |
| 4. C2×#22548651 | C2 | semidirect |
| 5. C2×#22548650 | C2 | semidirect |
| 6. C2×#108×C251 | C2 | semidirect |
| 17. #22548651 | C22 | semidirect |
| 18. #22548650 | C22 | semidirect |
| 21. #108×C251 | C22 | semidirect |
| 83. C2×C251 | #430 | semidirect |
| 86. C251 | C2×#430 | semidirect |
| 93. C2×#108 | D251 | semidirect |
| 108. #108 | C2×D251 | semidirect |
| 171. C2 | #30631734 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860793 | 2 |
| C2×M16×D251 | 2 |
| #30631734 | 2 |
| C2×#22548651 | 2 |
| C2×#22548650 | 2 |
| C2×#108×C251 | 2 |
| C2×#430 | 251 |