Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
516 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19104729 | C2 | semidirect |
| 3. #23781560 | C2 | semidirect |
| 4. #23781559 | C2 | semidirect |
| 5. #23781555 | C2 | semidirect |
| 6. C42×Dic163 | C2 | semidirect |
| 7. C2×#126×C163 | C2 | semidirect |
| 39. C42×C163 | D4 | semidirect |
| 74. Dic163 | #126 | semidirect |
| 80. C163 | #2860 | semidirect |
| 83. C2×#126 | D163 | semidirect |
| 120. C42 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104729 | 2 |
| #23781565 | 2 |
| #23781560 | 2 |
| #23781559 | 2 |
| #23781555 | 2 |
| C42×Dic163 | 2 |
| C2×#126×C163 | 2 |
| #2860 | 163 |