Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
332 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 9. C4×Dic326 | C4 | semidirect |
| 13. #19104658 | C4 | direct (N × H) |
| 43. Dic326 | C42 | semidirect |
| 69. C4×C163 | #103 | semidirect |
| 80. C163 | C4×#103 | semidirect |
| 152. C4 | #19104658 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic326 | 2 |
| C2×#19104658 | 2 |
| C2×C4×C163⋊C8 | 2 |
| #23781427 | 2 |
| C4×C4⋊C4×C163 | 2 |
| C4×#103 | 163 |