Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23782061 | C2 | semidirect |
| 2. #23781950 | C2 | semidirect |
| 4. #23781411 | C2 | semidirect |
| 5. Q8⋊(C163⋊C8) | C2 | semidirect |
| 61. Q8×C163 | SD16 | semidirect |
| 92. C163 | #1651 | semidirect |
| 150. Q8 | #14579687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782061 | 2 |
| #23781950 | 2 |
| #23781870 | 2 |
| #23781411 | 2 |
| Q8⋊(C163⋊C8) | 2 |
| D4⋊(C163⋊C8) | 2 |
| D4×Q8×C163 | 2 |
| #1651 | 163 |