Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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×#22551526 | C2 | semidirect |
| 4. #30656499 | C2 | semidirect |
| 5. C2×#107×C257 | C2 | semidirect |
| 10. C2×C8×D257 | C4 | semidirect |
| 69. C8×C257 | C22⋊C4 | semidirect |
| 83. C2×D257 | #107 | semidirect |
| 99. C257 | #1808 | semidirect |
| 103. C2×#107 | D257 | semidirect |
| 169. C8 | #16861595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D257 | 2 |
| C2×#22551526 | 2 |
| #30656594 | 2 |
| #30656499 | 2 |
| C2×#107×C257 | 2 |
| #1808 | 257 |