Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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. #41×Dic163 | C2 | semidirect |
| 2. #23781777 | C2 | semidirect |
| 3. #23781772 | C2 | semidirect |
| 4. #23781766 | C2 | semidirect |
| 5. #23781703 | C2 | semidirect |
| 6. #23781661 | C2 | semidirect |
| 7. C2×#19104645 | C2 | semidirect |
| 24. #135×C163 | C4 | semidirect |
| 42. #41×C163 | C2×C4 | semidirect |
| 48. Q16×C163 | C2×C4 | semidirect |
| 49. SD16×C163 | C2×C4 | semidirect |
| 50. D8×C163 | C2×C4 | semidirect |
| 51. C2×C8×C163 | C2×C4 | semidirect |
| 89. C163 | #2943 | semidirect |
| 100. #135 | Dic163 | semidirect |
| 120. #41 | C2×Dic163 | semidirect |
| 128. Q16 | C2×Dic163 | semidirect |
| 129. SD16 | C2×Dic163 | semidirect |
| 130. D8 | C2×Dic163 | semidirect |
| 133. C2×C8 | C2×Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic163 | 2 |
| #23781777 | 2 |
| #23781772 | 2 |
| #23781766 | 2 |
| #23781703 | 2 |
| #23781661 | 2 |
| C2×#19104645 | 2 |
| C2×#135×C163 | 2 |
| #2943 | 163 |