Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
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. #23756522 | C2 | semidirect |
| 2. C2×#19097546 | C2 | semidirect |
| 3. #23756504 | C2 | semidirect |
| 4. #23756432 | C2 | semidirect |
| 5. #23756414 | C2 | semidirect |
| 6. #23756413 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C313 | C2 | semidirect |
| 53. C313 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756522 | 2 |
| C2×#19097546 | 2 |
| #23756504 | 2 |
| #23756432 | 2 |
| #23756414 | 2 |
| #23756413 | 2 |
| AGL(1,ℤ/8)×C313 | 2 |
| #472 | 313 |