Finite Group DatabasebetaFinite Group DatabasebetaOrder 19904.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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. #23755733 | C2 | semidirect |
| 2. C2×#19097300 | C2 | semidirect |
| 3. #23755715 | C2 | semidirect |
| 4. #23755643 | C2 | semidirect |
| 5. #23755625 | C2 | semidirect |
| 6. #23755624 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C311 | C2 | semidirect |
| 53. C311 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23755733 | 2 |
| C2×#19097300 | 2 |
| #23755715 | 2 |
| #23755643 | 2 |
| #23755625 | 2 |
| #23755624 | 2 |
| AGL(1,ℤ/8)×C311 | 2 |
| #472 | 311 |