Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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×#19104671 | C2 | semidirect |
| 2. #23781708 | C2 | semidirect |
| 6. #23781433 | C2 | semidirect |
| 7. #424×C163 | C2 | semidirect |
| 97. C163 | #2063 | semidirect |
| 101. #424 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104671 | 2 |
| #23781708 | 2 |
| #23781669 | 2 |
| C2×#19104657 | 2 |
| C2×#19104651 | 2 |
| #23781433 | 2 |
| #424×C163 | 2 |
| #2063 | 163 |