Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23782172 | C2 | semidirect |
| 2. #23781682 | C2 | semidirect |
| 3. #23781628 | C2 | semidirect |
| 4. #23781422 | C2 | semidirect |
| 5. #575×C163 | C2 | semidirect |
| 35. C4×Dic163 | D4 | semidirect |
| 40. C2×Q8×C163 | D4 | semidirect |
| 42. C2×D4×C163 | D4 | semidirect |
| 49. C2×C8×C163 | D4 | semidirect |
| 98. C163 | #2010 | semidirect |
| 100. #575 | D163 | semidirect |
| 125. C2×Q8 | C22⋊D163 | semidirect |
| 128. C2×D4 | C22⋊D163 | semidirect |
| 142. C2×C8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782172 | 2 |
| #23781682 | 2 |
| #23781628 | 2 |
| #23781422 | 2 |
| #575×C163 | 2 |
| #2010 | 163 |