Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
752 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 181 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×#19104733 | C2 | semidirect |
| 3. C2×#19104724 | C2 | semidirect |
| 4. C2×#19104723 | C2 | semidirect |
| 5. C2×#19104722 | C2 | semidirect |
| 6. #23781565 | C2 | semidirect |
| 7. C42×Dic163 | C2 | semidirect |
| 8. C2×#124×C163 | C2 | semidirect |
| 47. C4×Dic163 | D4 | semidirect |
| 59. C42×C163 | D4 | semidirect |
| 106. Dic163 | #124 | semidirect |
| 113. C163 | #2858 | semidirect |
| 120. C2×#124 | D163 | semidirect |
| 173. C42 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104733 | 2 |
| C2×#19104731 | 2 |
| C2×#19104724 | 2 |
| C2×#19104723 | 2 |
| C2×#19104722 | 2 |
| #23781565 | 2 |
| C42×Dic163 | 2 |
| C2×#124×C163 | 2 |
| #2858 | 163 |