Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
872 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 237 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. #30656639 | C2 | semidirect |
| 4. #30656637 | C2 | semidirect |
| 5. #30656597 | C2 | semidirect |
| 6. #30656596 | C2 | semidirect |
| 7. #30656584 | C2 | semidirect |
| 8. C4×C22⋊C4×C257 | C2 | semidirect |
| 10. C2×#16861618 | C4 | semidirect |
| 60. Dic514 | C22⋊C4 | semidirect |
| 85. C2×C4×C257 | #41 | semidirect |
| 114. C257 | #2341 | semidirect |
| 123. C4×C22⋊C4 | D257 | semidirect |
| 200. C2×C4 | #16861618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16861618 | 2 |
| C2×C4×Dic514 | 2 |
| #30656639 | 2 |
| #30656637 | 2 |
| #30656597 | 2 |
| #30656596 | 2 |
| #30656584 | 2 |
| C4×C22⋊C4×C257 | 2 |
| #2341 | 257 |