Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23782072 | C2 | semidirect |
| 3. #23782069 | C2 | semidirect |
| 4. #23782066 | C2 | semidirect |
| 30. #14579683 | Q8 | semidirect |
| 42. C2×C8×C163 | Q8 | semidirect |
| 80. C163 | #3164 | semidirect |
| 114. C2×C8 | Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782293 | 2 |
| #23782072 | 2 |
| #23782069 | 2 |
| #23782066 | 2 |
| #23781708 | 2 |
| C2×#19104669 | 2 |
| #23781620 | 2 |
| #427×C163 | 2 |
| #3164 | 163 |