Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
272 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×C16×D163 | C2 | semidirect |
| 3. C22⋊(C163⋊C16) | C2 | semidirect |
| 4. (C2×D163)⋊C16 | C2 | semidirect |
| 5. C22⋊C16×C163 | C2 | semidirect |
| 13. C2×C163⋊C16 | C22 | semidirect |
| 16. C2×C16×C163 | C22 | semidirect |
| 40. C22×D163 | C16 | semidirect |
| 63. C22×C163 | C2×C16 | semidirect |
| 70. C2×D163 | C2×C16 | semidirect |
| 82. D163 | C22⋊C16 | direct (N × H) |
| 83. C163 | C2×C22⋊C16 | semidirect |
| 89. C22⋊C16 | D163 | direct (N × H) |
| 100. C2×C16 | C2×D163 | semidirect |
| 154. C22 | C16×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D163 | 2 |
| C2×C16×D163 | 2 |
| C22⋊(C163⋊C16) | 2 |
| (C2×D163)⋊C16 | 2 |
| C22⋊C16×C163 | 2 |
| C2×C22⋊C16 | 163 |