Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #23781569 | C2 | semidirect |
| 3. #23781557 | C2 | semidirect |
| 4. #23781555 | C2 | semidirect |
| 6. #23781539 | C2 | semidirect |
| 7. #23781536 | C2 | semidirect |
| 8. #23781531 | C2 | semidirect |
| 9. #382×C163 | C2 | semidirect |
| 13. #19104723 | C4 | semidirect |
| 35. C2×Dic326 | C2×C4 | semidirect |
| 51. (C2×D163)⋊C4 | C2×C4 | semidirect |
| 52. (C2×D163)⋊C4 | C2×C4 | semidirect |
| 61. C42×C163 | C2×C4 | semidirect |
| 127. C163 | #2379 | semidirect |
| 137. #382 | D163 | semidirect |
| 189. C42 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104723 | 2 |
| #23781569 | 2 |
| #23781557 | 2 |
| #23781555 | 2 |
| #23781543 | 2 |
| #23781539 | 2 |
| #23781536 | 2 |
| #23781531 | 2 |
| #382×C163 | 2 |
| #2379 | 163 |