Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
320 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 125 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. C4×#14579683 | C2 | semidirect |
| 3. #23781511 | C2 | semidirect |
| 4. #23781424 | C2 | semidirect |
| 8. #19104662 | C4 | semidirect |
| 13. C4×Q8×C163 | C4 | semidirect |
| 15. C4×D4×C163 | C4 | semidirect |
| 22. #14579683 | C2×C4 | semidirect |
| 25. C4×Dic163 | C2×C4 | semidirect |
| 82. C163 | #1759 | semidirect |
| 91. C4×Q8 | Dic163 | semidirect |
| 93. C4×D4 | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104662 | 2 |
| C4×#14579683 | 2 |
| #23781511 | 2 |
| #23781424 | 2 |
| C4×#41×C163 | 2 |
| #1759 | 163 |