Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#22551516 | C2 | semidirect |
| 5. #30656644 | C2 | semidirect |
| 6. #30656491 | C2 | semidirect |
| 7. C22×Q16×C257 | C2 | semidirect |
| 125. C257 | #2015 | semidirect |
| 127. C22×Q16 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16861605 | 2 |
| C2×#22551581 | 2 |
| C2×#22551516 | 2 |
| C2×#22551514 | 2 |
| #30656644 | 2 |
| #30656491 | 2 |
| C22×Q16×C257 | 2 |
| #2015 | 257 |