Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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. #30632261 | C2 | semidirect |
| 4. #30632080 | C2 | semidirect |
| 5. #30632072 | C2 | semidirect |
| 6. #30632065 | C2 | semidirect |
| 7. #30631642 | C2 | semidirect |
| 8. C22×Q16×C251 | C2 | semidirect |
| 96. C251 | #3156 | semidirect |
| 100. C22×Q16 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548746 | 2 |
| C2×#22548737 | 2 |
| #30632261 | 2 |
| #30632080 | 2 |
| #30632072 | 2 |
| #30632065 | 2 |
| #30631642 | 2 |
| C22×Q16×C251 | 2 |
| #3156 | 251 |