Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 792 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. C22×Q8×D163 | C2 | semidirect |
| 2. C22×#14579687 | C2 | semidirect |
| 4. #23781802 | C2 | direct (N × H) |
| 5. C2×#19104660 | C2 | semidirect |
| 6. C2×#19104659 | C2 | semidirect |
| 7. C2×(C2×D163)⋊C8 | C2 | semidirect |
| 8. C22×SD16×C163 | C2 | semidirect |
| 14. C2×Q8×D163 | C22 | semidirect |
| 19. C2×#14579687 | C22 | semidirect |
| 25. #19104660 | C22 | semidirect |
| 26. #19104659 | C22 | semidirect |
| 27. (C2×D163)⋊C8 | C22 | semidirect |
| 31. C2×SD16×C163 | C22 | semidirect |
| 38. C2×Dic326 | D4 | semidirect |
| 63. C2×Q8×C163 | D4 | semidirect |
| 76. C22×D163 | SD16 | semidirect |
| 81. Dic326 | C2×D4 | semidirect |
| 101. Q8×C163 | C2×D4 | semidirect |
| 123. C2×D163 | C2×SD16 | semidirect |
| 132. C2×C163 | #448 | semidirect |
| 137. C163 | C2×#448 | semidirect |
| 141. C22×SD16 | D163 | semidirect |
| 161. C2×SD16 | C2×D163 | semidirect |
| 184. C2×Q8 | C22⋊D163 | semidirect |
| 227. Q8 | C2×C22⋊D163 | semidirect |
| 271. C2 | #23781802 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D163 | 2 |
| C22×#14579687 | 2 |
| C2×#19104706 | 2 |
| #23781802 | 2 |
| C2×#19104660 | 2 |
| C2×#19104659 | 2 |
| C2×(C2×D163)⋊C8 | 2 |
| C22×SD16×C163 | 2 |
| C2×#448 | 163 |