Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
656 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 197 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. C22×#14579686 | C2 | semidirect |
| 3. #23782039 | C2 | direct (N × H) |
| 4. C2×C4×C163⋊C8 | C2 | semidirect |
| 5. C2×C4⋊Q8×C163 | C2 | semidirect |
| 9. C2×#14579686 | C22 | semidirect |
| 13. C4×C163⋊C8 | C22 | semidirect |
| 16. C4⋊Q8×C163 | C22 | semidirect |
| 26. C2×C163⋊C8 | D4 | semidirect |
| 43. C163⋊C8 | C2×D4 | semidirect |
| 49. C2×C4×C163 | SD16 | semidirect |
| 62. C4×C163 | C2×SD16 | semidirect |
| 64. C2×C163 | #492 | semidirect |
| 68. C163 | C2×#492 | semidirect |
| 71. C2×C4⋊Q8 | D163 | semidirect |
| 82. C4⋊Q8 | C2×D163 | semidirect |
| 117. C2×C4 | #14579686 | semidirect |
| 131. C4 | C2×#14579686 | semidirect |
| 134. C2 | #23782039 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579686 | 2 |
| C2×#19104732 | 2 |
| #23782039 | 2 |
| C2×C4×C163⋊C8 | 2 |
| C2×C4⋊Q8×C163 | 2 |
| C2×#492 | 163 |