Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
820 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 287 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×Q8×Dic257 | C2 | semidirect |
| 3. #30656643 | C2 | semidirect |
| 4. #30656642 | C2 | semidirect |
| 7. C2×C4×Q8×C257 | C2 | semidirect |
| 11. C2×Q8×D257 | C4 | semidirect |
| 38. #16861595 | Q8 | direct (N × H) |
| 64. C2×Dic257 | C2×Q8 | semidirect |
| 67. Q8×C257 | C22⋊C4 | semidirect |
| 76. C2×C4×C257 | C2×Q8 | semidirect |
| 90. C2×D257 | C4×Q8 | semidirect |
| 105. C257 | Q8×C22⋊C4 | semidirect |
| 109. C2×C4×Q8 | D257 | semidirect |
| 163. Q8 | #16861595 | direct (N × H) |
| 182. C2×C4 | Q8×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D257 | 2 |
| C2×Q8×Dic257 | 2 |
| #30656643 | 2 |
| #30656642 | 2 |
| #30656594 | 2 |
| C4×#16861595 | 2 |
| C2×C4×Q8×C257 | 2 |
| Q8×C22⋊C4 | 257 |