Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
668 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#14579688 | C2 | semidirect |
| 2. C22×D1304 | C2 | semidirect |
| 3. C2×#19104732 | C2 | semidirect |
| 4. C2×#19104723 | C2 | semidirect |
| 5. #23782054 | C2 | direct (N × H) |
| 6. C2×#97×C163 | C2 | semidirect |
| 12. C2×#14579688 | C22 | semidirect |
| 14. C2×D1304 | C22 | semidirect |
| 16. #19104732 | C22 | semidirect |
| 18. #19104723 | C22 | semidirect |
| 22. #97×C163 | C22 | semidirect |
| 43. C2×C8×C163 | D4 | semidirect |
| 69. C8×C163 | C2×D4 | semidirect |
| 83. C2×C163 | #496 | semidirect |
| 88. C163 | C2×#496 | semidirect |
| 95. C2×#97 | D163 | semidirect |
| 111. #97 | C2×D163 | semidirect |
| 131. C2×C8 | D652 | semidirect |
| 158. C8 | C2×D652 | semidirect |
| 174. C2 | #23782054 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579688 | 2 |
| C22×D1304 | 2 |
| C2×#19104732 | 2 |
| C2×#19104723 | 2 |
| #23782054 | 2 |
| C2×#97×C163 | 2 |
| C2×#496 | 163 |