Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
374 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C4×Dic514 | C2 | semidirect |
| 3. C2×#22551517 | C2 | semidirect |
| 6. #30656500 | C2 | semidirect |
| 7. #336×C257 | C2 | semidirect |
| 12. C2×#16861607 | C4 | semidirect |
| 72. Dic514 | C22⋊C4 | semidirect |
| 92. C2×C4×C257 | SD16 | semidirect |
| 132. C257 | #1880 | semidirect |
| 140. #336 | D257 | semidirect |
| 225. C2×C4 | #16861607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16861607 | 2 |
| C2×C4×Dic514 | 2 |
| C2×#22551517 | 2 |
| C2×#22551514 | 2 |
| #30656639 | 2 |
| #30656500 | 2 |
| #336×C257 | 2 |
| #1880 | 257 |