Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
740 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. C22×#16860800 | C2 | semidirect |
| 3. #30631842 | C2 | direct (N × H) |
| 4. C2×#22548638 | C2 | semidirect |
| 14. C2×#16860800 | C22 | semidirect |
| 16. #22548638 | C22 | semidirect |
| 64. C23×C251 | Q16 | semidirect |
| 85. C22×C251 | C2×Q16 | semidirect |
| 95. C2×C251 | #451 | semidirect |
| 99. C251 | C2×#451 | semidirect |
| 156. C23 | #16860800 | semidirect |
| 185. C22 | C2×#16860800 | semidirect |
| 195. C2 | #30631842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic502 | 2 |
| C22×#16860800 | 2 |
| #30631842 | 2 |
| C2×#22548638 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×C22⋊Q8×C251 | 2 |
| C2×#451 | 251 |