Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
872 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 275 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. #30656639 | C2 | semidirect |
| 4. #30656638 | C2 | semidirect |
| 5. #30656594 | C2 | semidirect |
| 6. C4×#16861595 | C2 | semidirect |
| 7. C2×C4×Q8×C257 | C2 | semidirect |
| 10. C2×#16861619 | C4 | semidirect |
| 65. C2×Dic257 | #41 | semidirect |
| 68. Q8×C257 | C22⋊C4 | semidirect |
| 77. C2×C4×C257 | #41 | semidirect |
| 106. C257 | #2341 | semidirect |
| 110. C2×C4×Q8 | D257 | semidirect |
| 164. Q8 | #16861595 | semidirect |
| 184. C2×C4 | #16861619 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16861619 | 2 |
| C2×Q8×Dic257 | 2 |
| #30656639 | 2 |
| #30656638 | 2 |
| #30656594 | 2 |
| C4×#16861595 | 2 |
| C2×C4×Q8×C257 | 2 |
| #2341 | 257 |