Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
820 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19104652 | C2 | semidirect |
| 2. #23781629 | C2 | semidirect |
| 4. C2×#14579683 | C22 | semidirect |
| 59. C22×C163 | #100 | semidirect |
| 69. C163 | #1783 | semidirect |
| 129. C22 | #19104652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104652 | 2 |
| #23781629 | 2 |
| C23×D4×C163 | 2 |
| #1783 | 163 |