Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
332 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23781721 | C2 | semidirect |
| 3. #23781409 | C2 | semidirect |
| 4. #23781408 | C2 | semidirect |
| 5. #331×C163 | C2 | semidirect |
| 12. C4⋊(C163⋊C8) | C22 | semidirect |
| 16. C4⋊C8×C163 | C22 | semidirect |
| 74. C163 | #1555 | semidirect |
| 80. #331 | D163 | semidirect |
| 89. C4⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×D163 | 2 |
| #23781721 | 2 |
| #23781409 | 2 |
| #23781408 | 2 |
| #331×C163 | 2 |
| #1555 | 163 |