Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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×#19104761 | C2 | semidirect |
| 2. #23782246 | C2 | semidirect |
| 3. C2×#19104663 | C2 | semidirect |
| 4. #23781434 | C2 | semidirect |
| 5. #390×C163 | C2 | semidirect |
| 32. #14579683 | D4 | semidirect |
| 40. C2×D4×C163 | D4 | semidirect |
| 101. C163 | #2006 | semidirect |
| 106. #390 | D163 | semidirect |
| 134. C2×D4 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| #23782246 | 2 |
| C2×#19104663 | 2 |
| #23781434 | 2 |
| #390×C163 | 2 |
| #2006 | 163 |