Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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 | semidirect |
| 3. C2×#19104678 | C2 | semidirect |
| 4. #23781477 | C2 | semidirect |
| 5. #23781471 | C2 | semidirect |
| 6. #23781449 | C2 | semidirect |
| 7. #473×C163 | C2 | semidirect |
| 18. #19104675 | C22 | semidirect |
| 19. C2×C163⋊C16 | C22 | semidirect |
| 21. C2×Q16×C163 | C22 | semidirect |
| 23. #108×C163 | C22 | semidirect |
| 91. C163 | #2194 | semidirect |
| 96. #473 | D163 | semidirect |
| 106. C2×Q16 | C2×D163 | semidirect |
| 115. #108 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782470 | 2 |
| #23782106 | 2 |
| C2×#19104678 | 2 |
| #23781477 | 2 |
| #23781471 | 2 |
| #23781449 | 2 |
| #473×C163 | 2 |
| #2194 | 163 |