Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#19104678 | C2 | semidirect |
| 2. C2×#19104676 | C2 | semidirect |
| 3. #23781901 | C2 | semidirect |
| 4. #23781469 | C2 | semidirect |
| 5. #23781466 | C2 | semidirect |
| 6. C22⋊(C163⋊C16) | C2 | semidirect |
| 7. C2×#135×C163 | C2 | semidirect |
| 39. Q16×C163 | D4 | semidirect |
| 42. D8×C163 | D4 | semidirect |
| 89. C163 | #2186 | semidirect |
| 91. C2×#135 | D163 | semidirect |
| 123. Q16 | C22⋊D163 | semidirect |
| 128. D8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104678 | 2 |
| C2×#19104676 | 2 |
| #23781901 | 2 |
| #23781469 | 2 |
| #23781466 | 2 |
| C22⋊(C163⋊C16) | 2 |
| C2×#135×C163 | 2 |
| #2186 | 163 |