Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
340 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 165 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. #23782074 | C2 | semidirect |
| 3. #23782067 | C2 | semidirect |
| 4. #23782063 | C2 | semidirect |
| 40. M16×C163 | Q8 | semidirect |
| 41. C2×C8×C163 | Q8 | semidirect |
| 75. C163 | #3163 | semidirect |
| 107. M16 | Dic326 | semidirect |
| 108. 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 |
| #23782074 | 2 |
| #23782067 | 2 |
| #23782063 | 2 |
| #23781707 | 2 |
| #23781703 | 2 |
| C2×#19104667 | 2 |
| #405×C163 | 2 |
| #3163 | 163 |