Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
578 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 578 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 |
|---|---|---|
| 1. #23782140 | C2 | semidirect |
| 2. C2×#19104650 | C2 | semidirect |
| 3. #23781521 | C2 | semidirect |
| 4. #23781431 | C2 | semidirect |
| 17. #120×C163 | C4 | semidirect |
| 22. C22×Dic163 | D4 | semidirect |
| 36. C24×C163 | C2×C4 | semidirect |
| 49. C22⋊C4×C163 | C2×C4 | semidirect |
| 71. C23×C163 | C22⋊C4 | semidirect |
| 84. C2×C4×C163 | C22⋊C4 | semidirect |
| 119. C163 | #1889 | semidirect |
| 130. #120 | Dic163 | semidirect |
| 145. C24 | C2×Dic163 | semidirect |
| 168. C22⋊C4 | C2×Dic163 | semidirect |
| 186. C23 | C22⋊Dic163 | semidirect |
| 204. C2×C4 | C22⋊Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782140 | 2 |
| C2×#19104650 | 2 |
| #23781521 | 2 |
| #23781431 | 2 |
| C2×#120×C163 | 2 |
| #1889 | 163 |