Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 370 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×#19104766 | C2 | semidirect |
| 3. C2×#19104663 | C2 | semidirect |
| 4. #23781434 | C2 | semidirect |
| 5. #391×C163 | C2 | semidirect |
| 32. #14579683 | D4 | semidirect |
| 39. C2×Q8×C163 | D4 | semidirect |
| 93. C163 | #2007 | semidirect |
| 98. #391 | D163 | semidirect |
| 122. C2×Q8 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104766 | 2 |
| #23782246 | 2 |
| C2×#19104663 | 2 |
| #23781434 | 2 |
| #391×C163 | 2 |
| #2007 | 163 |