Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
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×#22576186 | C2 | semidirect |
| 2. #31774475 | C2 | semidirect |
| 3. C2×#22576087 | C2 | semidirect |
| 4. C2×#22576086 | C2 | semidirect |
| 5. #31773800 | C2 | semidirect |
| 6. #31773665 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8)×C271 | C2 | semidirect |
| 45. #16864638 | D4 | semidirect |
| 68. C2×D4×C271 | D4 | semidirect |
| 74. M16×C271 | D4 | semidirect |
| 152. C271 | #2006 | semidirect |
| 155. C2×AGL(1,ℤ/8) | D271 | semidirect |
| 205. C2×D4 | C22⋊D271 | semidirect |
| 218. M16 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576186 | 2 |
| #31774475 | 2 |
| C2×#22576087 | 2 |
| C2×#22576086 | 2 |
| #31773800 | 2 |
| #31773665 | 2 |
| C2×AGL(1,ℤ/8)×C271 | 2 |
| #2006 | 271 |