Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. C2×#22551625 | C2 | semidirect |
| 2. C2×#22551622 | C2 | semidirect |
| 4. C2×#22551520 | C2 | semidirect |
| 5. #30656643 | C2 | semidirect |
| 6. #30656505 | C2 | semidirect |
| 7. C2×#104×C257 | C2 | semidirect |
| 41. C2×Dic514 | D4 | semidirect |
| 53. #16861602 | D4 | semidirect |
| 71. M16×C257 | D4 | semidirect |
| 144. C257 | #2007 | semidirect |
| 150. C2×#104 | D257 | semidirect |
| 210. M16 | C22⋊D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551625 | 2 |
| C2×#22551622 | 2 |
| #30657315 | 2 |
| C2×#22551520 | 2 |
| #30656643 | 2 |
| #30656505 | 2 |
| C2×#104×C257 | 2 |
| #2007 | 257 |