Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
738 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 173 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×#19104766 | C2 | semidirect |
| 3. #23781821 | C2 | semidirect |
| 4. #23781804 | C2 | semidirect |
| 5. #23781674 | C2 | semidirect |
| 6. #23781629 | C2 | semidirect |
| 7. C23×Q8×C163 | C2 | semidirect |
| 10. C2×#14579689 | C22 | semidirect |
| 11. C2×#14579686 | C22 | semidirect |
| 19. #19104659 | C22 | semidirect |
| 51. C2×Q8×C163 | D4 | semidirect |
| 93. C22×C163 | #137 | semidirect |
| 108. C163 | #3004 | semidirect |
| 110. C23×Q8 | D163 | semidirect |
| 146. C2×Q8 | C22⋊D163 | semidirect |
| 204. C22 | #19104766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104766 | 2 |
| #23782176 | 2 |
| #23781821 | 2 |
| #23781804 | 2 |
| #23781674 | 2 |
| #23781629 | 2 |
| C23×Q8×C163 | 2 |
| #3004 | 163 |