Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
438 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C4×D652 | C2 | semidirect |
| 3. C2×#19104656 | C2 | semidirect |
| 4. C2×#19104655 | C2 | semidirect |
| 5. #23781427 | C2 | semidirect |
| 6. #23781420 | C2 | semidirect |
| 7. #390×C163 | C2 | semidirect |
| 12. C2×#14579684 | C4 | semidirect |
| 43. C2×C163⋊C8 | C2×C4 | semidirect |
| 53. C2×D4×C163 | C2×C4 | semidirect |
| 74. D652 | C22⋊C4 | semidirect |
| 101. C2×C4×C163 | D8 | semidirect |
| 146. C163 | #1879 | semidirect |
| 152. #390 | D163 | semidirect |
| 186. C2×D4 | C4×D163 | semidirect |
| 246. C2×C4 | #14579684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579684 | 2 |
| C2×C4×D652 | 2 |
| C2×#19104656 | 2 |
| C2×#19104655 | 2 |
| #23781427 | 2 |
| #23781420 | 2 |
| #390×C163 | 2 |
| #1879 | 163 |