Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
840 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 205 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×#19104711 | C2 | semidirect |
| 3. #23781584 | C2 | semidirect |
| 4. #23781576 | C2 | semidirect |
| 5. #23781572 | C2 | semidirect |
| 7. #23781538 | C2 | semidirect |
| 8. #23781525 | C2 | semidirect |
| 9. C23×Q8×C163 | C2 | semidirect |
| 34. C2×C22⋊D163 | Q8 | semidirect |
| 55. C2×Q8×C163 | D4 | semidirect |
| 67. C22×D163 | C2×Q8 | semidirect |
| 78. C2×Dic163 | C2×Q8 | semidirect |
| 101. C22×C163 | C22⋊Q8 | semidirect |
| 126. C163 | #2409 | semidirect |
| 128. C23×Q8 | D163 | semidirect |
| 165. C2×Q8 | C22⋊D163 | semidirect |
| 233. C22 | #19104711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104711 | 2 |
| C2×C4×C22⋊D163 | 2 |
| #23781584 | 2 |
| #23781576 | 2 |
| #23781572 | 2 |
| #23781544 | 2 |
| #23781538 | 2 |
| #23781525 | 2 |
| C23×Q8×C163 | 2 |
| #2409 | 163 |