Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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. #30656634 | C2 | semidirect |
| 4. #30656632 | C2 | semidirect |
| 12. C2×#16861597 | C4 | semidirect |
| 53. C2×Dic257 | C4⋊C4 | semidirect |
| 94. C257 | #2316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551548 | 2 |
| C22×#16861597 | 2 |
| #30656634 | 2 |
| #30656632 | 2 |
| #30656597 | 2 |
| #30656595 | 2 |
| #380×C257 | 2 |
| #2316 | 257 |