Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 3. #23782074 | C2 | semidirect |
| 4. #23782070 | C2 | semidirect |
| 5. #23782063 | C2 | semidirect |
| 50. M16×C163 | Q8 | semidirect |
| 74. C8×C163 | C2×Q8 | semidirect |
| 92. C163 | #3165 | semidirect |
| 131. M16 | Dic326 | semidirect |
| 167. C8 | C2×Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782222 | 2 |
| C2×#19104735 | 2 |
| #23782074 | 2 |
| #23782070 | 2 |
| #23782063 | 2 |
| #23781707 | 2 |
| C4×M16×C163 | 2 |
| #3165 | 163 |