Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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×#16861608 | C2 | semidirect |
| 3. C2×#22551511 | C2 | semidirect |
| 4. C2×#22551510 | C2 | semidirect |
| 6. #30656501 | C2 | semidirect |
| 122. C257 | #2020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551622 | 2 |
| C22×#16861608 | 2 |
| C2×#22551511 | 2 |
| C2×#22551510 | 2 |
| #30656704 | 2 |
| #30656501 | 2 |
| C2×#137×C257 | 2 |
| #2020 | 257 |