Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23782106 | C2 | direct (N × H) |
| 3. C2×#19104681 | C2 | semidirect |
| 4. C2×#19104678 | C2 | semidirect |
| 5. C2×#19104675 | C2 | semidirect |
| 6. C22×Q16×C163 | C2 | semidirect |
| 13. #19104681 | C22 | semidirect |
| 14. #19104678 | C22 | semidirect |
| 15. #19104675 | C22 | semidirect |
| 21. C2×Q16×C163 | C22 | semidirect |
| 80. C2×C163 | #510 | semidirect |
| 83. C163 | C2×#510 | semidirect |
| 86. C22×Q16 | D163 | semidirect |
| 99. C2×Q16 | C2×D163 | semidirect |
| 165. C2 | #23782106 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104757 | 2 |
| #23782106 | 2 |
| C2×#19104681 | 2 |
| C2×#19104678 | 2 |
| C2×#19104675 | 2 |
| C22×Q16×C163 | 2 |
| C2×#510 | 163 |