Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782380 | C2 | semidirect |
| 2. #23782320 | C2 | semidirect |
| 3. #23782063 | C2 | semidirect |
| 4. #23781988 | C2 | semidirect |
| 5. #23781982 | C2 | semidirect |
| 6. #23781955 | C2 | semidirect |
| 7. #23781945 | C2 | semidirect |
| 8. #23781915 | C2 | semidirect |
| 9. #23781744 | C2 | semidirect |
| 10. #23781706 | C2 | semidirect |
| 11. C4×D8×C163 | C2 | semidirect |
| 101. C8×C163 | #41 | semidirect |
| 127. C163 | #3354 | semidirect |
| 137. C4×D8 | D163 | semidirect |
| 229. C8 | #14579699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782380 | 2 |
| #23782320 | 2 |
| #23782063 | 2 |
| #23781988 | 2 |
| #23781982 | 2 |
| #23781955 | 2 |
| #23781945 | 2 |
| #23781915 | 2 |
| #23781744 | 2 |
| #23781706 | 2 |
| C4×D8×C163 | 2 |
| #3354 | 163 |