Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22551618 | C2 | semidirect |
| 2. #30657315 | C2 | semidirect |
| 3. C2×#22551519 | C2 | semidirect |
| 4. C2×#22551518 | C2 | semidirect |
| 5. #30656640 | C2 | semidirect |
| 6. #30656505 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8)×C257 | C2 | semidirect |
| 45. #16861602 | D4 | semidirect |
| 68. C2×D4×C257 | D4 | semidirect |
| 74. M16×C257 | D4 | semidirect |
| 152. C257 | #2006 | semidirect |
| 155. C2×AGL(1,ℤ/8) | D257 | semidirect |
| 205. C2×D4 | C22⋊D257 | semidirect |
| 218. M16 | C22⋊D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551618 | 2 |
| #30657315 | 2 |
| C2×#22551519 | 2 |
| C2×#22551518 | 2 |
| #30656640 | 2 |
| #30656505 | 2 |
| C2×AGL(1,ℤ/8)×C257 | 2 |
| #2006 | 257 |