Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 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. #23782300 | C2 | semidirect |
| 2. #23781852 | C2 | semidirect |
| 3. #23781458 | C2 | semidirect |
| 4. #23781453 | C2 | semidirect |
| 5. #453×C163 | C2 | semidirect |
| 13. #19104650 | C22 | semidirect |
| 14. H(5,𝔽2)×C163 | C22 | semidirect |
| 18. #100×C163 | C22 | semidirect |
| 20. C23×D163 | D4 | semidirect |
| 30. C22⋊Dic163 | D4 | semidirect |
| 38. C2×D4×C163 | D4 | semidirect |
| 43. C42×C163 | D4 | semidirect |
| 95. C163 | #2196 | semidirect |
| 99. #453 | D163 | semidirect |
| 102. H(5,𝔽2) | C2×D163 | semidirect |
| 112. #100 | C2×D163 | semidirect |
| 127. C2×D4 | C22⋊D163 | semidirect |
| 139. C42 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782300 | 2 |
| #23781852 | 2 |
| #23781458 | 2 |
| #23781453 | 2 |
| #453×C163 | 2 |
| #2196 | 163 |