Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#19104783 | C2 | semidirect |
| 2. #23782465 | C2 | semidirect |
| 3. #23782239 | C2 | semidirect |
| 4. #23781850 | C2 | semidirect |
| 5. #23781840 | C2 | semidirect |
| 6. #23781681 | C2 | semidirect |
| 7. C2×#101×C163 | C2 | semidirect |
| 17. #19104768 | C22 | semidirect |
| 19. #19104763 | C22 | semidirect |
| 21. #19104733 | C22 | semidirect |
| 22. #19104724 | C22 | semidirect |
| 26. #19104661 | C22 | semidirect |
| 29. #101×C163 | C22 | semidirect |
| 123. C163 | #3020 | semidirect |
| 131. C2×#101 | D163 | semidirect |
| 153. #101 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104783 | 2 |
| #23782465 | 2 |
| #23782239 | 2 |
| #23781850 | 2 |
| #23781840 | 2 |
| #23781681 | 2 |
| C2×#101×C163 | 2 |
| #3020 | 163 |